Pub Date : 2024-09-28DOI: 10.1016/j.physd.2024.134386
V. Teplov, V. Bessonov, V. Bessonova, A. Telegin
Micromagnetic modeling of non-linear autoresonance magnetization oscillations in thin films of yttrium iron garnet (YIG) with specified growth directions is conducted. It is found that in the case of rapid frequency modulation (sweep rate of the order of 1016 Hz/sec) of 1Oe excitation magnetic field, the maximum precession angle of magnetization can achieve up to 160°. For the first time, the influence of demagnetization fields, magneto-crystalline anisotropy, and Gilbert damping on autoresonance phenomena in YIG films is numerically calculated. It is shown that demagnetization fields and damping have a weak influence on parameters of autoresonance. Simultaneously, damping provides a shorter phase-locking time between the excitation field and intrinsic magnetization oscillations in the film, favoring high amplitude of magnetization oscillations. The magneto-crystalline anisotropy leads to a reduction of the threshold sweep rate of the pumping field for YIG films with [100] direction, as well as the emergence of parametric instability for [210] films. The results of the work are aimed to be applied for the experimental observation of autoresonance phenomena in thin yttrium iron garnet films.
{"title":"Incorporating magneto-crystalline anisotropy and damping in the autoresonance oscillations modeling in thin YIG films","authors":"V. Teplov, V. Bessonov, V. Bessonova, A. Telegin","doi":"10.1016/j.physd.2024.134386","DOIUrl":"10.1016/j.physd.2024.134386","url":null,"abstract":"<div><div>Micromagnetic modeling of non-linear autoresonance magnetization oscillations in thin films of yttrium iron garnet (YIG) with specified growth directions is conducted. It is found that in the case of rapid frequency modulation (sweep rate of the order of 1016 Hz/sec) of 1Oe excitation magnetic field, the maximum precession angle of magnetization can achieve up to 160°. For the first time, the influence of demagnetization fields, magneto-crystalline anisotropy, and Gilbert damping on autoresonance phenomena in YIG films is numerically calculated. It is shown that demagnetization fields and damping have a weak influence on parameters of autoresonance. Simultaneously, damping provides a shorter phase-locking time between the excitation field and intrinsic magnetization oscillations in the film, favoring high amplitude of magnetization oscillations. The magneto-crystalline anisotropy leads to a reduction of the threshold sweep rate of the pumping field for YIG films with [100] direction, as well as the emergence of parametric instability for [210] films. The results of the work are aimed to be applied for the experimental observation of autoresonance phenomena in thin yttrium iron garnet films.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-23DOI: 10.1016/j.physd.2024.134384
Keke Pei , Yongzhen Pei , Changguo Li
The dynamics of systems composed of cyclically competing species are complicated by the fact that they are strongly influenced by fluctuations. For this reason, it is attractive to study low-dimensional cycles where these impacts are most prominent. In this paper, we investigate the impacts of asymmetric compared to symmetric reactive rates on three-species biological diversity and spatial pattern formation in a four-state case using an RPS game model on a one-dimensional lattice. In addition, we also discuss the effects of interference thresholds on biodiversity maintenance when species are impulsively disturbed under both symmetric and asymmetric rates. The results show that enhancement of the competition rate promotes biodiversity while the mobility rate has the opposite effect when these rates being symmetric. Meanwhile, changes in reproductive rates have no direct effect on biodiversity. If rates are asymmetric, only one species survives and biodiversity is negatively affected. Conversely, the outcome of single species survival is altered when species are impulsively disturbed. Under symmetric rates, an increase in interference threshold results in a shift from coexistence of three species to survival of two species. With asymmetric rates, population dynamics change from the survival of only one species to the survival of two species if the interference is introduced. Our findings may enlighten people by RPS game model to protect endangered animals, or kill off harmful species, or to engineer cyclical population to stabilize the functionality of gene circuits for cancer treatment, or to guide election campaign.
{"title":"Effects of asymmetric rates and impulse interference in Rock-Paper-Scissors games","authors":"Keke Pei , Yongzhen Pei , Changguo Li","doi":"10.1016/j.physd.2024.134384","DOIUrl":"10.1016/j.physd.2024.134384","url":null,"abstract":"<div><div>The dynamics of systems composed of cyclically competing species are complicated by the fact that they are strongly influenced by fluctuations. For this reason, it is attractive to study low-dimensional cycles where these impacts are most prominent. In this paper, we investigate the impacts of asymmetric compared to symmetric reactive rates on three-species biological diversity and spatial pattern formation in a four-state case using an RPS game model on a one-dimensional lattice. In addition, we also discuss the effects of interference thresholds on biodiversity maintenance when species are impulsively disturbed under both symmetric and asymmetric rates. The results show that enhancement of the competition rate promotes biodiversity while the mobility rate has the opposite effect when these rates being symmetric. Meanwhile, changes in reproductive rates have no direct effect on biodiversity. If rates are asymmetric, only one species survives and biodiversity is negatively affected. Conversely, the outcome of single species survival is altered when species are impulsively disturbed. Under symmetric rates, an increase in interference threshold results in a shift from coexistence of three species to survival of two species. With asymmetric rates, population dynamics change from the survival of only one species to the survival of two species if the interference is introduced. Our findings may enlighten people by RPS game model to protect endangered animals, or kill off harmful species, or to engineer cyclical population to stabilize the functionality of gene circuits for cancer treatment, or to guide election campaign.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-22DOI: 10.1016/j.physd.2024.134380
QingShan Tan, Jian Zhang
In this paper, the Riemann problem for the defocusing Kundu–Eckhaus equation is investigated by Whitham modulation theory. First, we study the dispersion relation for linear waves. Then, the zero-phase and one-phase periodic solutions of the Kundu–Eckhaus equation along with the corresponding Whitham modulation equations are derived by the finite-gap integration method. Further, employing the Whitham equations parametrized by the Riemann invariants, the main fundamental wave structures induced by the discontinuous initial data are found. Analytical and graphic methods are utilized to provide the wave structures of rarefaction waves and dispersive shock waves, and thus for a complete classification of solutions under general step-like conditions of initial discontinuity.
{"title":"Whitham modulation theory and Riemann problem for the Kundu–Eckhaus equation","authors":"QingShan Tan, Jian Zhang","doi":"10.1016/j.physd.2024.134380","DOIUrl":"10.1016/j.physd.2024.134380","url":null,"abstract":"<div><div>In this paper, the Riemann problem for the defocusing Kundu–Eckhaus equation is investigated by Whitham modulation theory. First, we study the dispersion relation for linear waves. Then, the zero-phase and one-phase periodic solutions of the Kundu–Eckhaus equation along with the corresponding Whitham modulation equations are derived by the finite-gap integration method. Further, employing the Whitham equations parametrized by the Riemann invariants, the main fundamental wave structures induced by the discontinuous initial data are found. Analytical and graphic methods are utilized to provide the wave structures of rarefaction waves and dispersive shock waves, and thus for a complete classification of solutions under general step-like conditions of initial discontinuity.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-22DOI: 10.1016/j.physd.2024.134387
Cherie Gautam, Maitri Verma
The rise in atmospheric carbon dioxide () concentration has led to a rise in the global average surface temperatures. Deforestation and infrastructure expansion are key contributors to the increase in level. This study presents a non-linear mathematical model to explore the impact of infrastructure expansion on deforestation and rise in the atmospheric concentration. The proposed model considers the growth of infrastructure activities, driven by the increasing population, which in turn reduces the carrying capacity of forest biomass. The model is qualitatively analyzed to examine the system’s behavior in long run. It is found that a high growth rate of infrastructure expansion results in lower equilibrium level of forest biomass and higher concentrations. Moreover, for high population growth driven by infrastructure expansion, exceeding a critical level of infrastructure growth rate can cause the system to lose stability and generation of limit cycle oscillations through a supercritical Hopf-bifurcation. An increase in the growth rate coefficient of human population due to infrastructure expansion activities and deforestation rate can also lead to stability loss of interior equilibrium and existence of limit cycle oscillations in the system via Hopf-bifurcation. It is noticed that for critically high deforestation rate, the system may enter into transcritical bifurcation, resulting in the extinction of forest biomass. The study is extended to derive the strategies to effectively leverage existing mitigation options to reduce emissions from infrastructure expansion by taking efficiencies of mitigation options to cut the carbon dioxide emission rate and reduce the declination rate of carrying capacity of forest biomass resulting from infrastructure expansion as time-dependent control variables.
{"title":"Mathematical modeling of emission and control of carbon dioxide from infrastructure expansion activities","authors":"Cherie Gautam, Maitri Verma","doi":"10.1016/j.physd.2024.134387","DOIUrl":"10.1016/j.physd.2024.134387","url":null,"abstract":"<div><div>The rise in atmospheric carbon dioxide (<span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>) concentration has led to a rise in the global average surface temperatures. Deforestation and infrastructure expansion are key contributors to the increase in <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> level. This study presents a non-linear mathematical model to explore the impact of infrastructure expansion on deforestation and rise in the atmospheric <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> concentration. The proposed model considers the growth of infrastructure activities, driven by the increasing population, which in turn reduces the carrying capacity of forest biomass. The model is qualitatively analyzed to examine the system’s behavior in long run. It is found that a high growth rate of infrastructure expansion results in lower equilibrium level of forest biomass and higher <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> concentrations. Moreover, for high population growth driven by infrastructure expansion, exceeding a critical level of infrastructure growth rate can cause the system to lose stability and generation of limit cycle oscillations through a supercritical Hopf-bifurcation. An increase in the growth rate coefficient of human population due to infrastructure expansion activities and deforestation rate can also lead to stability loss of interior equilibrium and existence of limit cycle oscillations in the system via Hopf-bifurcation. It is noticed that for critically high deforestation rate, the system may enter into transcritical bifurcation, resulting in the extinction of forest biomass. The study is extended to derive the strategies to effectively leverage existing mitigation options to reduce <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> emissions from infrastructure expansion by taking efficiencies of mitigation options to cut the carbon dioxide emission rate and reduce the declination rate of carrying capacity of forest biomass resulting from infrastructure expansion as time-dependent control variables.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.physd.2024.134373
Mustafa Turkyilmazoglu , Abdulaziz Alotaibi
This paper investigates the fluid flow phenomenon arising from the combined action of two parallel plates, which can expand/squeeze, absorb/inject, and stretch/shrink at different rates. These physical mechanisms are incorporated into the governing unsteady Navier–Stokes equations, which are then reduced to a fourth-order nonlinear differential equation with boundary conditions reflecting the imposed wall constraints. By letting the permeable Reynolds number (controlling the nonlinear convective terms) limit to zero, we demonstrate the existence of exact solutions expressed in terms of advanced mathematical functions. Additionally, in the absence of wall expansion/contraction, elementary exponential solutions are obtained under particular relationships between the stretching/shrinking and permeability parameters. A shear-like exact solution with broader applicability across various physical parameters is also identified. For moderate values of the expansion/squeezing parameters and permeable Reynolds numbers, we propose an efficient double-expansion perturbation analysis to approximate the flow behavior. Otherwise, for general physical parameters, a comprehensive mathematical analysis is provided and numerical simulations are employed to extract insights into the complex fluid motion between the parallel plates.
{"title":"Fluid flow between two parallel active plates","authors":"Mustafa Turkyilmazoglu , Abdulaziz Alotaibi","doi":"10.1016/j.physd.2024.134373","DOIUrl":"10.1016/j.physd.2024.134373","url":null,"abstract":"<div><div>This paper investigates the fluid flow phenomenon arising from the combined action of two parallel plates, which can expand/squeeze, absorb/inject, and stretch/shrink at different rates. These physical mechanisms are incorporated into the governing unsteady Navier–Stokes equations, which are then reduced to a fourth-order nonlinear differential equation with boundary conditions reflecting the imposed wall constraints. By letting the permeable Reynolds number (controlling the nonlinear convective terms) limit to zero, we demonstrate the existence of exact solutions expressed in terms of advanced mathematical functions. Additionally, in the absence of wall expansion/contraction, elementary exponential solutions are obtained under particular relationships between the stretching/shrinking and permeability parameters. A shear-like exact solution with broader applicability across various physical parameters is also identified. For moderate values of the expansion/squeezing parameters and permeable Reynolds numbers, we propose an efficient double-expansion perturbation analysis to approximate the flow behavior. Otherwise, for general physical parameters, a comprehensive mathematical analysis is provided and numerical simulations are employed to extract insights into the complex fluid motion between the parallel plates.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.physd.2024.134348
N. Qwabe , K.S. Govinder
Complex networks of proteins and genes control cell growth until mitosis. These components play crucial roles in determining the characteristics and timing of each reaction in the cell. A family of cyclins and cyclin-dependent kinases regulates the progression of the cell from one stage to the next, while certain inhibitors regulate cell proliferation, significantly impacting this process. We examine the impact of p53 protein production in the cyclin E/cyclin-dependent kinase 2 (CycE/CDK2) subsystem. Although the precise functioning of the p53 protein is not fully understood, it is known to exhibit pulsatile behaviour, triggered in response to DNA damage. Consequently, the expression of the p53 protein within the cell system increases with the severity of DNA damage. Similarly, levels of CycE/CDK2 are substantially elevated in instances of DNA damage.
To investigate this subsystem, we have developed a mathematical model of the CycE/CDK2 subsystem, presented as non-linear ordinary differential equations. Our primary aim is to determine the conditions that could theoretically result in tumorigenesis. We conduct a dynamical systems analysis to investigate the presence of stable limit cycles, which indicate the standard operational states of cells. Our investigation reveals the levels of p53 protein at which the cell can correct defects, undergo apoptosis, or enter quiescence, and where the system exhibits a Hopf-bifurcation (limit cycles). This is the novelty of our study, as previous research has primarily focused on numerical simulations.
Using MATLAB simulations, we produced various results in response to different expressions and concentrations of the p53 protein, allowing us to assess its influence on malignant cells. By altering the concentration of protein p53, we ascertain the specific cellular circumstances that facilitate its natural growth, self-correction in the presence of defective activity, and entry into a state of quiescence.
This investigation is motivated by the significant role of oscillations in driving, controlling, and managing the cellular oversight machinery. These aspects are incorporated into developing a mathematical model that emulates cellular operations. From this research, we establish that E2F is a critical target to mitigate oncogenic activity, achievable by managing the pulsatile behaviour of the inhibitor p53 or inhibiting its production process within the cell machinery.
{"title":"A mathematical treatment of the impact of p53 signalling on the expression of the transcription factor E2F in the CycE/Cdk2 subsystem in cancerous cells","authors":"N. Qwabe , K.S. Govinder","doi":"10.1016/j.physd.2024.134348","DOIUrl":"10.1016/j.physd.2024.134348","url":null,"abstract":"<div><div>Complex networks of proteins and genes control cell growth until mitosis. These components play crucial roles in determining the characteristics and timing of each reaction in the cell. A family of cyclins and cyclin-dependent kinases regulates the progression of the cell from one stage to the next, while certain inhibitors regulate cell proliferation, significantly impacting this process. We examine the impact of p53 protein production in the cyclin E/cyclin-dependent kinase 2 (CycE/CDK2) subsystem. Although the precise functioning of the p53 protein is not fully understood, it is known to exhibit pulsatile behaviour, triggered in response to DNA damage. Consequently, the expression of the p53 protein within the cell system increases with the severity of DNA damage. Similarly, levels of CycE/CDK2 are substantially elevated in instances of DNA damage.</div><div>To investigate this subsystem, we have developed a mathematical model of the CycE/CDK2 subsystem, presented as non-linear ordinary differential equations. Our primary aim is to determine the conditions that could theoretically result in tumorigenesis. We conduct a dynamical systems analysis to investigate the presence of stable limit cycles, which indicate the standard operational states of cells. Our investigation reveals the levels of p53 protein at which the cell can correct defects, undergo apoptosis, or enter quiescence, and where the system exhibits a Hopf-bifurcation (limit cycles). This is the novelty of our study, as previous research has primarily focused on numerical simulations.</div><div>Using MATLAB simulations, we produced various results in response to different expressions and concentrations of the p53 protein, allowing us to assess its influence on malignant cells. By altering the concentration of protein p53, we ascertain the specific cellular circumstances that facilitate its natural growth, self-correction in the presence of defective activity, and entry into a state of quiescence.</div><div>This investigation is motivated by the significant role of oscillations in driving, controlling, and managing the cellular oversight machinery. These aspects are incorporated into developing a mathematical model that emulates cellular operations. From this research, we establish that E2F is a critical target to mitigate oncogenic activity, achievable by managing the pulsatile behaviour of the inhibitor p53 or inhibiting its production process within the cell machinery.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.physd.2024.134385
Andrei D. Werkhausen, Heyder Hey
In this paper, we revisit Sundman’s Theorem on the three-body problem. We provide a simple example demonstrating that the requirement on the total angular momentum (bounded away from zero) can be relaxed for a particular set of initial conditions, allowing double shocks. We present an explicit solution for the exact triple-collision scenario through a Sundman-like formal regularization.
在本文中，我们重温了关于三体问题的桑德曼定理。我们提供了一个简单的例子，证明对于一组特定的初始条件，可以放宽对总角动量 L 的要求（远离零的边界），允许双冲击。我们通过类似桑德曼的形式正则化，提出了精确三体碰撞情形的明确解法。
{"title":"Sundman theorem revisited","authors":"Andrei D. Werkhausen, Heyder Hey","doi":"10.1016/j.physd.2024.134385","DOIUrl":"10.1016/j.physd.2024.134385","url":null,"abstract":"<div><div>In this paper, we revisit Sundman’s Theorem on the three-body problem. We provide a simple example demonstrating that the requirement on the total angular momentum <span><math><mi>L</mi></math></span> (bounded away from zero) can be relaxed for a particular set of initial conditions, allowing double shocks. We present an explicit solution for the exact triple-collision scenario through a Sundman-like formal regularization.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers a modified Leslie–Gower prey–predator reaction–diffusion model introducing harvesting of both species. Both the temporal and spatiotemporal dynamics of the model have been examined. We have found the stability regions and drawn bifurcation diagrams to determine the harvesting effect on the model, revealing that the harvesting has a stabilizing effect. Local bifurcations, such as transcritical and Hopf bifurcations, appear in the temporal system. For the spatiotemporal model, Turing instability conditions have been determined. The amplitude equation for the critical modes has been derived using multiple time scale analyses by taking the harvesting effort as the bifurcating parameter. Also, we have verified the theoretical results by plotting several kinds of stationary patterns, including stripes, spots, and a mix of stripes and spots. This study’s critical observation is that as harvesting effort rises, the patterns steadily turn into spots, i.e., harvesting influences pattern creation strongly. This fosters a dynamic equilibrium, allowing competitors to maintain distance, optimize resource use and survive.
{"title":"Spatiotemporal analysis of a modified Leslie–Gower model with cross-diffusion and harvesting","authors":"Samir Biswas, Lakpa Thendup Bhutia, Tapan Kumar Kar, Bidhan Bhunia, Esita Das","doi":"10.1016/j.physd.2024.134381","DOIUrl":"10.1016/j.physd.2024.134381","url":null,"abstract":"<div><p>This paper considers a modified Leslie–Gower prey–predator reaction–diffusion model introducing harvesting of both species. Both the temporal and spatiotemporal dynamics of the model have been examined. We have found the stability regions and drawn bifurcation diagrams to determine the harvesting effect on the model, revealing that the harvesting has a stabilizing effect. Local bifurcations, such as transcritical and Hopf bifurcations, appear in the temporal system. For the spatiotemporal model, Turing instability conditions have been determined. The amplitude equation for the critical modes has been derived using multiple time scale analyses by taking the harvesting effort as the bifurcating parameter. Also, we have verified the theoretical results by plotting several kinds of stationary patterns, including stripes, spots, and a mix of stripes and spots. This study’s critical observation is that as harvesting effort rises, the patterns steadily turn into spots, i.e., harvesting influences pattern creation strongly. This fosters a dynamic equilibrium, allowing competitors to maintain distance, optimize resource use and survive.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-18DOI: 10.1016/j.physd.2024.134354
Qi Cheng , Jun Zhang , Weinian Zhang
Beverton–Holt Ricker competition model is a planar difference system that describes intraspecific competition among individuals and interspecific competition. Known works investigated the stability of equilibria in some cases, showed the existence of stable 2-periodic points when there are no interior equilibria, and found numerically an attractor with riddled basin of attraction for some appropriate parameters. In this paper, we prove the existence of the global attractor, and give a complete description on qualitative properties and bifurcations of all equilibria except for some cases of high degeneracy. Moreover, we obtain different kinds of 1-dimensional or 2-dimensional structures of the global attractor, which were not considered in the known work.
{"title":"Global attractor and its 1D and 2D structures of Beverton–Holt Ricker competition model","authors":"Qi Cheng , Jun Zhang , Weinian Zhang","doi":"10.1016/j.physd.2024.134354","DOIUrl":"10.1016/j.physd.2024.134354","url":null,"abstract":"<div><p>Beverton–Holt Ricker competition model is a planar difference system that describes intraspecific competition among individuals and interspecific competition. Known works investigated the stability of equilibria in some cases, showed the existence of stable 2-periodic points when there are no interior equilibria, and found numerically an attractor with riddled basin of attraction for some appropriate parameters. In this paper, we prove the existence of the global attractor, and give a complete description on qualitative properties and bifurcations of all equilibria except for some cases of high degeneracy. Moreover, we obtain different kinds of 1-dimensional or 2-dimensional structures of the global attractor, which were not considered in the known work.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-17DOI: 10.1016/j.physd.2024.134363
Weixin Yan, Zhen Wang, Yang Liu
This paper investigates the issue of multistability in state-dependent switched neural networks (SSNNs) with Mexican-hat-type activation functions (AFs). It establishes the coexistence and stability of multiple equilibrium points (EPs). Initially, the state space is partitioned based on the geometric characteristics of the Mexican-hat-type AF, enabling to determine the positions of the EPs. Secondly, the coexistence of EPs for -neurons SSNNs under specific sufficient conditions is proved with the Brouwer’s fixed-point theorem. Next, by using diagonally dominant matrix theory and Gershgorin circle theorem, it is proven that there are asymptotically stable EPs under some conditions, where and are nonnegative integers satisfying . Therefore, we can obtain that SSNNs can have larger storage capacity by selecting the appropriate parameters . Finally, the correctness of the results in this paper is verified through two numerical examples.
{"title":"Multistability of state-dependent switched neural networks with Mexican-hat-type activation functions","authors":"Weixin Yan, Zhen Wang, Yang Liu","doi":"10.1016/j.physd.2024.134363","DOIUrl":"10.1016/j.physd.2024.134363","url":null,"abstract":"<div><p>This paper investigates the issue of multistability in state-dependent switched neural networks (SSNNs) with Mexican-hat-type activation functions (AFs). It establishes the coexistence and stability of multiple equilibrium points (EPs). Initially, the state space is partitioned based on the geometric characteristics of the Mexican-hat-type AF, enabling to determine the positions of the EPs. Secondly, the coexistence of <span><math><mrow><msup><mrow><mn>9</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><msup><mrow><mn>7</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><msup><mrow><mn>5</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msup><msup><mrow><mn>3</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></msup></mrow></math></span> EPs for <span><math><mi>n</mi></math></span>-neurons SSNNs under specific sufficient conditions is proved with the Brouwer’s fixed-point theorem. Next, by using diagonally dominant matrix theory and Gershgorin circle theorem, it is proven that there are <span><math><mrow><msup><mrow><mn>5</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><msup><mrow><mn>4</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><msup><mrow><mn>3</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msup><msup><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></msup></mrow></math></span> asymptotically stable EPs under some conditions, where <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> are nonnegative integers satisfying <span><math><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>+</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>≤</mo><mi>n</mi></mrow></math></span>. Therefore, we can obtain that SSNNs can have larger storage capacity by selecting the appropriate parameters <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></math></span>. Finally, the correctness of the results in this paper is verified through two numerical examples.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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