Pub Date : 2023-12-11DOI: 10.1142/s0218127423501821
M. Al-Kaff, H. El-Metwally, El-Metwally M. Elabbasy, Abd-Elalim A. Elsadany
This paper presents a discrete predator–prey interaction model involving hibernating vertebrates, with detailed analysis and simulation. Hibernation contributes to the survival and reproduction of organisms and species in the ecosystem as a whole. In addition, it also constitutes a wise sharing of time, space, and resources with others. We have created a new predator–prey model by integrating the two species, Holling-III and Holling-I, which have a bifurcation within a specified parameter range. We discovered that this system possesses the stability of fixed points as well as several bifurcation behaviors. To accomplish this, the center manifold theorem and bifurcation theory are applied to create existence conditions for period-doubling bifurcations and Neimark–Sacker bifurcations, which are depicted in the graph as distinct structures. Examples of numerical simulations include bifurcation diagrams, maximum Lyapunov exponents, and phase portraits, which demonstrate not just the validity of theoretical analysis but also complex dynamical behaviors and biological processes. Finally, the Ott–Grebogi–Yorke (OGY) method and phases of chaos control bifurcation were used to control the chaos of predator–prey model in hibernating vertebrates.
{"title":"Dynamic Behaviors in a Discrete Model for Predator–Prey Interactions Involving Hibernating Vertebrates","authors":"M. Al-Kaff, H. El-Metwally, El-Metwally M. Elabbasy, Abd-Elalim A. Elsadany","doi":"10.1142/s0218127423501821","DOIUrl":"https://doi.org/10.1142/s0218127423501821","url":null,"abstract":"This paper presents a discrete predator–prey interaction model involving hibernating vertebrates, with detailed analysis and simulation. Hibernation contributes to the survival and reproduction of organisms and species in the ecosystem as a whole. In addition, it also constitutes a wise sharing of time, space, and resources with others. We have created a new predator–prey model by integrating the two species, Holling-III and Holling-I, which have a bifurcation within a specified parameter range. We discovered that this system possesses the stability of fixed points as well as several bifurcation behaviors. To accomplish this, the center manifold theorem and bifurcation theory are applied to create existence conditions for period-doubling bifurcations and Neimark–Sacker bifurcations, which are depicted in the graph as distinct structures. Examples of numerical simulations include bifurcation diagrams, maximum Lyapunov exponents, and phase portraits, which demonstrate not just the validity of theoretical analysis but also complex dynamical behaviors and biological processes. Finally, the Ott–Grebogi–Yorke (OGY) method and phases of chaos control bifurcation were used to control the chaos of predator–prey model in hibernating vertebrates.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"37 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139010236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s0218127423501778
Dongya Xu, Hongjun Liu
The strength of a cryptosystem relies on the security of its key expansion algorithm, which is an important component of a block cipher. However, numerous block ciphers exhibit the vulnerability of reversibility and serialization. Therefore, it is necessary to design an irreversible parallel key expansion algorithm to generate independent round keys. First, a 2D nondegenerate exponential chaotic map (2D-NECM) is constructed, and the results of the dynamic analysis show that the 2D-NECM possesses ergodicity and superior randomness within a large range of parameters. Then, an irreversible parallel key expansion algorithm is designed based on 2D-NECM and primitive polynomial over GF([Formula: see text]). By injecting random perturbation into the initial key, the algorithm can generate different round keys even if the same initial key is used. Simulation results indicate that the algorithm has high security performance. It effectively satisfies the requirements of irreversibility and parallelism, while ensuring the mutual independence of round keys.
{"title":"A Strong Key Expansion Algorithm Based on Nondegenerate 2D Chaotic Map Over GF(2n)","authors":"Dongya Xu, Hongjun Liu","doi":"10.1142/s0218127423501778","DOIUrl":"https://doi.org/10.1142/s0218127423501778","url":null,"abstract":"The strength of a cryptosystem relies on the security of its key expansion algorithm, which is an important component of a block cipher. However, numerous block ciphers exhibit the vulnerability of reversibility and serialization. Therefore, it is necessary to design an irreversible parallel key expansion algorithm to generate independent round keys. First, a 2D nondegenerate exponential chaotic map (2D-NECM) is constructed, and the results of the dynamic analysis show that the 2D-NECM possesses ergodicity and superior randomness within a large range of parameters. Then, an irreversible parallel key expansion algorithm is designed based on 2D-NECM and primitive polynomial over GF([Formula: see text]). By injecting random perturbation into the initial key, the algorithm can generate different round keys even if the same initial key is used. Simulation results indicate that the algorithm has high security performance. It effectively satisfies the requirements of irreversibility and parallelism, while ensuring the mutual independence of round keys.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"143 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138981422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s0218127423501808
Chenyu Liang, Hangjun Zhang, Yancong Xu, Libin Rong
In this paper, we investigated the dynamics of the interaction between Microcystis aeruginosa and filter-feeding fish in a new aquatic ecological model and considered the effects of aggregation and harvesting and focused on studying the critical threshold conditions through the analysis of saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation. We also conducted numerical simulations to illustrate our findings and provided biological interpretations. The results obtained indicate that the aggregation effect or harvesting can disrupt the coexistence of Microcystis aeruginosa and filter-feeding fish. The filter-feeding fish population may go extinct while the Microcystis aeruginosa population could survive. We identified the importance of finding an appropriate timing for harvesting Microcystis aeruginosa in order to promote the growth of the filter-feeding fish population. This optimal timing may be influenced by the carrying capacity of Microcystis aeruginosa. Taken together, our study sheds light on the dynamics of Microcystis aeruginosa and filter-feeding fish in an aquatic ecosystem, highlighting the critical role of aggregation, harvesting, and timing in determining the coexistence and survival of these species.
{"title":"Bifurcation Analysis of a New Aquatic Ecological Model with Aggregation Effect and Harvesting","authors":"Chenyu Liang, Hangjun Zhang, Yancong Xu, Libin Rong","doi":"10.1142/s0218127423501808","DOIUrl":"https://doi.org/10.1142/s0218127423501808","url":null,"abstract":"In this paper, we investigated the dynamics of the interaction between Microcystis aeruginosa and filter-feeding fish in a new aquatic ecological model and considered the effects of aggregation and harvesting and focused on studying the critical threshold conditions through the analysis of saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation. We also conducted numerical simulations to illustrate our findings and provided biological interpretations. The results obtained indicate that the aggregation effect or harvesting can disrupt the coexistence of Microcystis aeruginosa and filter-feeding fish. The filter-feeding fish population may go extinct while the Microcystis aeruginosa population could survive. We identified the importance of finding an appropriate timing for harvesting Microcystis aeruginosa in order to promote the growth of the filter-feeding fish population. This optimal timing may be influenced by the carrying capacity of Microcystis aeruginosa. Taken together, our study sheds light on the dynamics of Microcystis aeruginosa and filter-feeding fish in an aquatic ecosystem, highlighting the critical role of aggregation, harvesting, and timing in determining the coexistence and survival of these species.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"72 4","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138979039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s0218127423501754
Mingshan Li, Naiming Xie, Xiaoliang Zhou
In this paper, we investigate the complex dynamics of a mapping derived from a differential equation with simple time-periodic delay. Firstly, we calculate the truncated normal form of 1:1 resonance of the mapping at a degenerate fixed point and obtain an approximating system of the mapping by using Picard iteration. By analyzing the approximate system, we find that the mapping will undergo a 1:1 resonance at the degenerate fixed point. Secondly, the qualitative property and the stability of the degenerate fixed point are determined, which provide a new view to understand the dynamic of differential equation with simple time-periodic delay. However, the approximate system does not have the versal unfolding of the Bogdanov–Takens singularity of codimension 2. These phenomena show that simple time-periodic delay can support complex dynamics. Finally, a numerical simulation is carried out to verify the analytic results.
{"title":"Simple Time-Periodic Delay Can Support Complex Dynamics","authors":"Mingshan Li, Naiming Xie, Xiaoliang Zhou","doi":"10.1142/s0218127423501754","DOIUrl":"https://doi.org/10.1142/s0218127423501754","url":null,"abstract":"In this paper, we investigate the complex dynamics of a mapping derived from a differential equation with simple time-periodic delay. Firstly, we calculate the truncated normal form of 1:1 resonance of the mapping at a degenerate fixed point and obtain an approximating system of the mapping by using Picard iteration. By analyzing the approximate system, we find that the mapping will undergo a 1:1 resonance at the degenerate fixed point. Secondly, the qualitative property and the stability of the degenerate fixed point are determined, which provide a new view to understand the dynamic of differential equation with simple time-periodic delay. However, the approximate system does not have the versal unfolding of the Bogdanov–Takens singularity of codimension 2. These phenomena show that simple time-periodic delay can support complex dynamics. Finally, a numerical simulation is carried out to verify the analytic results.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"105 s1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138978500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s0218127423501857
Shihui Fu, Joseph Páez Chávez, Qishao Lu
In this paper, we consider the piecewise-linear Chua’s circuit, which is well known for its rich variety of bifurcation, chaotic and other nonlinear phenomena. Suitable switching boundaries are introduced based on the piecewise-linear representation of Chua’s diode. In this way, we derive analytical conditions for a grazing bifurcation to occur, when one or two families of periodic orbits have a zero-velocity contact with the switching boundaries. In connection to this phenomenon, we also study the focus-center-limit cycle bifurcation and its implications regarding the system dynamics, from both analytical and numerical points of view. Furthermore, a detailed parametric study of Chua’s circuit is carried out via path-following techniques for nonsmooth dynamical systems, implemented via the continuation software COCO. This study reveals the presence of codimension-one bifurcations of limit cycles, such as those mentioned above, as well as classical (fold and period-doubling) bifurcations. The analysis confirms the presence of coexisting attractors, which are produced by a hysteresis loop induced by the interaction of a fold and a focus-center-limit cycle bifurcation.
{"title":"Grazing-Induced Dynamics of the Piecewise-Linear Chua’s Circuit","authors":"Shihui Fu, Joseph Páez Chávez, Qishao Lu","doi":"10.1142/s0218127423501857","DOIUrl":"https://doi.org/10.1142/s0218127423501857","url":null,"abstract":"In this paper, we consider the piecewise-linear Chua’s circuit, which is well known for its rich variety of bifurcation, chaotic and other nonlinear phenomena. Suitable switching boundaries are introduced based on the piecewise-linear representation of Chua’s diode. In this way, we derive analytical conditions for a grazing bifurcation to occur, when one or two families of periodic orbits have a zero-velocity contact with the switching boundaries. In connection to this phenomenon, we also study the focus-center-limit cycle bifurcation and its implications regarding the system dynamics, from both analytical and numerical points of view. Furthermore, a detailed parametric study of Chua’s circuit is carried out via path-following techniques for nonsmooth dynamical systems, implemented via the continuation software COCO. This study reveals the presence of codimension-one bifurcations of limit cycles, such as those mentioned above, as well as classical (fold and period-doubling) bifurcations. The analysis confirms the presence of coexisting attractors, which are produced by a hysteresis loop induced by the interaction of a fold and a focus-center-limit cycle bifurcation.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"79 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138978618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s0218127423300380
Basil Alattar, M. Ghommem, Vladimir Puzyrev
In this paper, we integrate deep learning techniques with the motion-induced current method to analyze the nonlinear response of electrostatic MEMS resonators consisting of vibrating beams under electrostatic actuation. The motion-induced current method relies on a transduction mechanism that converts the motion of the resonator to a current signal. The third harmonic of the induced current captures the motion characteristics of the MEMS resonator. We conduct electrical measurements on a MEMS device comprising a microcantilever beam subject to electrostatic actuation using a side electrode. The electrical measurements are verified against their optical counterparts to confirm the suitability of the motion-induced current method to analyze the motion of the MEMS resonator. Next, we develop a model by combining deep learning methods with experimental data aiming to detect the nonlinear dynamics associated with the motion of the resonator when subjected to large actuation voltages. The results demonstrate high prediction accuracy of the data-driven model in terms of capturing the peak resonance, the onset of bifurcation, the occurrence hysteresis and its bandwidth.
{"title":"Deep Learning for Nonlinear Characterization of Electrostatic Vibrating Beam MEMS","authors":"Basil Alattar, M. Ghommem, Vladimir Puzyrev","doi":"10.1142/s0218127423300380","DOIUrl":"https://doi.org/10.1142/s0218127423300380","url":null,"abstract":"In this paper, we integrate deep learning techniques with the motion-induced current method to analyze the nonlinear response of electrostatic MEMS resonators consisting of vibrating beams under electrostatic actuation. The motion-induced current method relies on a transduction mechanism that converts the motion of the resonator to a current signal. The third harmonic of the induced current captures the motion characteristics of the MEMS resonator. We conduct electrical measurements on a MEMS device comprising a microcantilever beam subject to electrostatic actuation using a side electrode. The electrical measurements are verified against their optical counterparts to confirm the suitability of the motion-induced current method to analyze the motion of the MEMS resonator. Next, we develop a model by combining deep learning methods with experimental data aiming to detect the nonlinear dynamics associated with the motion of the resonator when subjected to large actuation voltages. The results demonstrate high prediction accuracy of the data-driven model in terms of capturing the peak resonance, the onset of bifurcation, the occurrence hysteresis and its bandwidth.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"74 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138979005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s0218127423300367
L. Moysis, M. Lawnik, Christos Volos
This work presents a numerical method to color the bifurcation diagram of any discrete map, based on the distribution of the map’s values in its domain. This density-colored diagram reveals information on the uniformity of the map’s value distribution across its domain set, as a bifurcation parameter is increased. This diagram can serve as a complementary visual tool for the analysis of chaotic maps, and can be vital for the application of chaotic dynamics.
{"title":"Density-Colored Bifurcation Diagrams — A Complementary Tool for Chaotic Map Analysis","authors":"L. Moysis, M. Lawnik, Christos Volos","doi":"10.1142/s0218127423300367","DOIUrl":"https://doi.org/10.1142/s0218127423300367","url":null,"abstract":"This work presents a numerical method to color the bifurcation diagram of any discrete map, based on the distribution of the map’s values in its domain. This density-colored diagram reveals information on the uniformity of the map’s value distribution across its domain set, as a bifurcation parameter is increased. This diagram can serve as a complementary visual tool for the analysis of chaotic maps, and can be vital for the application of chaotic dynamics.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"155 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138981367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s021812742350181x
Yafei Cao, Hongjun Liu, Dongya Xu
To solve the problem of finite precision effect of existing chaotic maps on digital platform, first, a nondegenerate 2D integer-domain hyperchaotic map (2D-IDHCM) over GF([Formula: see text]) is constructed. Then, the proof that 2D-IDHCM satisfies Devaney’s definition of chaos and the proof of boundedness of Lyapunov exponents are given. The analytic results of dynamic behaviors demonstrate that 2D-IDHCM has ergodicity and large Lyapunov exponents within a certain parameter range, and without dynamic degradation. Finally, to verify the practicality of 2D-IDHCM, a keyed hash function based on 2D-IDHCM is designed, which can absorb variable-length message and generates 256, 512, 1024-bit or longer hash values in parallel. The experimental results demonstrate that 2D-IDHCM has better dynamic behaviors, and can be used in practical applications.
{"title":"Constructing a Nondegenerate 2D Integer-Domain Hyperchaotic Map Over GF(2n) with Application in Parallel Hashing","authors":"Yafei Cao, Hongjun Liu, Dongya Xu","doi":"10.1142/s021812742350181x","DOIUrl":"https://doi.org/10.1142/s021812742350181x","url":null,"abstract":"To solve the problem of finite precision effect of existing chaotic maps on digital platform, first, a nondegenerate 2D integer-domain hyperchaotic map (2D-IDHCM) over GF([Formula: see text]) is constructed. Then, the proof that 2D-IDHCM satisfies Devaney’s definition of chaos and the proof of boundedness of Lyapunov exponents are given. The analytic results of dynamic behaviors demonstrate that 2D-IDHCM has ergodicity and large Lyapunov exponents within a certain parameter range, and without dynamic degradation. Finally, to verify the practicality of 2D-IDHCM, a keyed hash function based on 2D-IDHCM is designed, which can absorb variable-length message and generates 256, 512, 1024-bit or longer hash values in parallel. The experimental results demonstrate that 2D-IDHCM has better dynamic behaviors, and can be used in practical applications.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"26 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138980013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s0218127423501766
Wenshuo Li, Xiaofeng Wang
In this paper, we focus on a class of optimal eighth-order iterative methods, initially proposed by Sharma et al., whose second step can choose any fourth-order iterative method. By selecting the first two steps as an optimal fourth-order iterative method, we derive an optimal eighth-order one-parameter iterative method, which can solve nonlinear systems. Employing fractal theory, we investigate the dynamic behavior of rational operators associated with the iterative method through the Scaling theorem and Möbius transformation. Subsequently, we conduct a comprehensive study of the chaotic dynamics and stability of the iterative method. Our analysis involves the examination of strange fixed points and their stability, critical points, and the parameter spaces generated on the complex plane with critical points as initial points. We utilize these findings to intuitively select parameter values from the figures. Furthermore, we generate dynamical planes for the selected parameter values and ultimately determine the range of unstable parameter values, thus obtaining the range of stable parameter values. The bifurcation diagram shows the influence of parameter selection on the iteration sequence. In addition, by drawing attractive basins, it can be seen that this iterative method is superior to the same-order iterative method in terms of convergence speed and average iterations. Finally, the matrix sign function, nonlinear equation and nonlinear system are solved by this iterative method, which shows the applicability of this iterative method.
{"title":"An Optimal Eighth-Order One-Parameter Single-Root Finder: Chaotic Dynamics and Stability Analysis","authors":"Wenshuo Li, Xiaofeng Wang","doi":"10.1142/s0218127423501766","DOIUrl":"https://doi.org/10.1142/s0218127423501766","url":null,"abstract":"In this paper, we focus on a class of optimal eighth-order iterative methods, initially proposed by Sharma et al., whose second step can choose any fourth-order iterative method. By selecting the first two steps as an optimal fourth-order iterative method, we derive an optimal eighth-order one-parameter iterative method, which can solve nonlinear systems. Employing fractal theory, we investigate the dynamic behavior of rational operators associated with the iterative method through the Scaling theorem and Möbius transformation. Subsequently, we conduct a comprehensive study of the chaotic dynamics and stability of the iterative method. Our analysis involves the examination of strange fixed points and their stability, critical points, and the parameter spaces generated on the complex plane with critical points as initial points. We utilize these findings to intuitively select parameter values from the figures. Furthermore, we generate dynamical planes for the selected parameter values and ultimately determine the range of unstable parameter values, thus obtaining the range of stable parameter values. The bifurcation diagram shows the influence of parameter selection on the iteration sequence. In addition, by drawing attractive basins, it can be seen that this iterative method is superior to the same-order iterative method in terms of convergence speed and average iterations. Finally, the matrix sign function, nonlinear equation and nonlinear system are solved by this iterative method, which shows the applicability of this iterative method.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"91 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138981540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.1142/s0218127423501742
Qian Cao, Xiongxiong Bao
In this paper, we are concerned with a diffusive templator model in chemical self-replication, which describes the process of an individual molecule duplicating itself. Firstly, the stability of non-negative constant equilibrium solution is introduced. Then the existence of Hopf bifurcation is proved. Particularly, the stability and the direction of Hopf bifurcation for the spatially homogeneous model are discussed. Furthermore, by space decomposition and implicit function theorem, it is shown that the system may undergo a steady-state bifurcation with a two-dimensional kernel. Finally, several numerical simulations are completed to demonstrate the theoretical results.
{"title":"Bifurcation Solutions to the Templator Model in Chemical Self-Replication","authors":"Qian Cao, Xiongxiong Bao","doi":"10.1142/s0218127423501742","DOIUrl":"https://doi.org/10.1142/s0218127423501742","url":null,"abstract":"In this paper, we are concerned with a diffusive templator model in chemical self-replication, which describes the process of an individual molecule duplicating itself. Firstly, the stability of non-negative constant equilibrium solution is introduced. Then the existence of Hopf bifurcation is proved. Particularly, the stability and the direction of Hopf bifurcation for the spatially homogeneous model are discussed. Furthermore, by space decomposition and implicit function theorem, it is shown that the system may undergo a steady-state bifurcation with a two-dimensional kernel. Finally, several numerical simulations are completed to demonstrate the theoretical results.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"6 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138981216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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