Pub Date : 2022-05-14DOI: 10.15388/namc.2022.27.27535
Jia Liu, Yun Kang
This paper concerned with a diffusive predator–prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we derive some results on the existence and nonexistence of nonconstant steady states of this model by considering the effect of diffusion. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can also induce the chaos in the system.
{"title":"Spatiotemporal dynamics of a diffusive predator–prey model with fear effect","authors":"Jia Liu, Yun Kang","doi":"10.15388/namc.2022.27.27535","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27535","url":null,"abstract":"This paper concerned with a diffusive predator–prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we derive some results on the existence and nonexistence of nonconstant steady states of this model by considering the effect of diffusion. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can also induce the chaos in the system.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41381612","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 : 2022-05-10DOI: 10.15388/namc.2022.27.27491
Xinguang Zhang, Dezhou Kong, Hui Tian, Yonghong Wu, B. Wiwatanapataphee
In this paper, we are concerned with the eigenvalue problem of Hadamard-type singular fractional differential equations with multi-point boundary conditions. By constructing the upper and lower solutions of the eigenvalue problem and using the properties of the Green function, the eigenvalue interval of the problem is established via Schauder’s fixed point theorem. The main contribution of this work is on tackling the nonlinearity which possesses singularity on some space variables.
{"title":"An upper-lower solution method for the eigenvalue problem of Hadamard-type singular fractional differential equation","authors":"Xinguang Zhang, Dezhou Kong, Hui Tian, Yonghong Wu, B. Wiwatanapataphee","doi":"10.15388/namc.2022.27.27491","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27491","url":null,"abstract":"In this paper, we are concerned with the eigenvalue problem of Hadamard-type singular fractional differential equations with multi-point boundary conditions. By constructing the upper and lower solutions of the eigenvalue problem and using the properties of the Green function, the eigenvalue interval of the problem is established via Schauder’s fixed point theorem. The main contribution of this work is on tackling the nonlinearity which possesses singularity on some space variables.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43282084","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 : 2022-05-10DOI: 10.15388/namc.2022.27.27493
E. Erdoğan, A. Ferrer-Sapena, E. Jiménez-Fernández
We analyze the basic structure of certain metric models, which are constituted by an index I acting on a metric space (D; d) representing a relevant property of the elements of D. We call such a structure (D; d; I) an index space and define on it normalization and consistency constants that measure to what extent I is compatible with the metric d. The “best” indices are those with such constants equal to 1 (standard indices), and we show an approximation method for other indices using them. With the help of Lipschitz extensions, we show how to apply these tools: a new model for the triage process in the emergency department of a hospital is presented.
{"title":"Index spaces and standard indices in metric modelling","authors":"E. Erdoğan, A. Ferrer-Sapena, E. Jiménez-Fernández","doi":"10.15388/namc.2022.27.27493","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27493","url":null,"abstract":"We analyze the basic structure of certain metric models, which are constituted by an index I acting on a metric space (D; d) representing a relevant property of the elements of D. We call such a structure (D; d; I) an index space and define on it normalization and consistency constants that measure to what extent I is compatible with the metric d. The “best” indices are those with such constants equal to 1 (standard indices), and we show an approximation method for other indices using them. With the help of Lipschitz extensions, we show how to apply these tools: a new model for the triage process in the emergency department of a hospital is presented.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48259783","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 : 2022-05-09DOI: 10.15388/namc.2022.27.27486
L. S. Ramya, R. Sakthivel, Chao Wang
This paper investigates the finite-time stabilization problem of fractional-order nonlinear differential systems via an asymmetrically saturated reliable control in the sense of Caputo’s fractional derivative. In particular, an asymmetrical saturation control problem is converted to a symmetrical saturation control problem by using a linear matrix inequality framework criterion to achieve the essential results. Specifically, in this paper, we obtain two sets of sufficient conditions under different scenarios of structured uncertainty, namely, norm-bounded parametric uncertainty and linear fractional transformation uncertainty. The uncertainty considered in this paper is a combination of polytopic form and structured form. With the help of control theories of fractional-order system and linear matrix inequality technique, some sufficient criteria to ensure reliable finite-time stability of fractional-order differential systems by using the indirect Lyapunov approach are derived. As a final point, the derived criteria are numerically validated by means of examples based on financial fractional-order differential system and permanent magnet synchronous motor chaotic fractional-order differential system.
{"title":"Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties","authors":"L. S. Ramya, R. Sakthivel, Chao Wang","doi":"10.15388/namc.2022.27.27486","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27486","url":null,"abstract":"This paper investigates the finite-time stabilization problem of fractional-order nonlinear differential systems via an asymmetrically saturated reliable control in the sense of Caputo’s fractional derivative. In particular, an asymmetrical saturation control problem is converted to a symmetrical saturation control problem by using a linear matrix inequality framework criterion to achieve the essential results. Specifically, in this paper, we obtain two sets of sufficient conditions under different scenarios of structured uncertainty, namely, norm-bounded parametric uncertainty and linear fractional transformation uncertainty. The uncertainty considered in this paper is a combination of polytopic form and structured form. With the help of control theories of fractional-order system and linear matrix inequality technique, some sufficient criteria to ensure reliable finite-time stability of fractional-order differential systems by using the indirect Lyapunov approach are derived. As a final point, the derived criteria are numerically validated by means of examples based on financial fractional-order differential system and permanent magnet synchronous motor chaotic fractional-order differential system.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48682066","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 : 2022-05-05DOI: 10.15388/namc.2022.27.27473
Jiazhe Lin, Jiapeng Li, R. Xu
It is well known that integer-order neural networks with diffusion have rich spatial and temporal dynamical behaviors, including Turing pattern and Hopf bifurcation. Recently, some studies indicate that fractional calculus can depict the memory and hereditary attributes of neural networks more accurately. In this paper, we mainly investigate the Turing pattern in a delayed reaction–diffusion neural network with Caputo-type fractional derivative. In particular, we find that this fractional neural network can form steadily spatial patterns even if its first-derivative counterpart cannot develop any steady pattern, which implies that temporal fractional derivative contributes to pattern formation. Numerical simulations show that both fractional derivative and time delay have influence on the shape of Turing patterns.
{"title":"Turing instability and pattern formation of a fractional Hopfield reaction–diffusion neural network with transmission delay","authors":"Jiazhe Lin, Jiapeng Li, R. Xu","doi":"10.15388/namc.2022.27.27473","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27473","url":null,"abstract":"It is well known that integer-order neural networks with diffusion have rich spatial and temporal dynamical behaviors, including Turing pattern and Hopf bifurcation. Recently, some studies indicate that fractional calculus can depict the memory and hereditary attributes of neural networks more accurately. In this paper, we mainly investigate the Turing pattern in a delayed reaction–diffusion neural network with Caputo-type fractional derivative. In particular, we find that this fractional neural network can form steadily spatial patterns even if its first-derivative counterpart cannot develop any steady pattern, which implies that temporal fractional derivative contributes to pattern formation. Numerical simulations show that both fractional derivative and time delay have influence on the shape of Turing patterns.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46077644","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 : 2022-05-02DOI: 10.15388/namc.2022.27.27446
Zhengbo Chang, Xinzhu Meng, T. Hayat, A. Hobiny
We propose a stochastic SIR model with two different diseases cross-infection and immunization. The model incorporates the effects of stochasticity, cross-infection rate and immunization. By using stochastic analysis and Khasminski ergodicity theory, the existence and boundedness of the global positive solution about the epidemic model are firstly proved. Subsequently, we theoretically carry out the sufficient conditions of stochastic extinction and persistence of the diseases. Thirdly, the existence of ergodic stationary distribution is proved. The results reveal that white noise can affect the dynamics of the system significantly. Finally, the numerical simulation is made and consistent with the theoretical results.
{"title":"Modeling and analysis of SIR epidemic dynamics in immunization and cross-infection environments: Insights from a stochastic model","authors":"Zhengbo Chang, Xinzhu Meng, T. Hayat, A. Hobiny","doi":"10.15388/namc.2022.27.27446","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27446","url":null,"abstract":"We propose a stochastic SIR model with two different diseases cross-infection and immunization. The model incorporates the effects of stochasticity, cross-infection rate and immunization. By using stochastic analysis and Khasminski ergodicity theory, the existence and boundedness of the global positive solution about the epidemic model are firstly proved. Subsequently, we theoretically carry out the sufficient conditions of stochastic extinction and persistence of the diseases. Thirdly, the existence of ergodic stationary distribution is proved. The results reveal that white noise can affect the dynamics of the system significantly. Finally, the numerical simulation is made and consistent with the theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47747974","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 : 2022-04-27DOI: 10.15388/namc.2022.27.27417
Chuangxia Huang, Bingwen Liu, Hedi Yang, Jinde Cao
This article involves a kind of shunting inhibitory cellular neural networks incorporating D operator and mixed delays. First of all, we demonstrate that, under appropriate external input conditions, some positive solutions of the addressed system exist globally. Secondly, with the help of the differential inequality techniques and exploiting Lyapunov functional approach, some criteria are established to evidence the globally exponential stability on the positive almost periodic solutions. Eventually, a numerical case is provided to test and verify the correctness and reliability of the proposed findings.
{"title":"Positive almost periodicity on SICNNs incorporating mixed delays and D operator","authors":"Chuangxia Huang, Bingwen Liu, Hedi Yang, Jinde Cao","doi":"10.15388/namc.2022.27.27417","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27417","url":null,"abstract":"This article involves a kind of shunting inhibitory cellular neural networks incorporating D operator and mixed delays. First of all, we demonstrate that, under appropriate external input conditions, some positive solutions of the addressed system exist globally. Secondly, with the help of the differential inequality techniques and exploiting Lyapunov functional approach, some criteria are established to evidence the globally exponential stability on the positive almost periodic solutions. Eventually, a numerical case is provided to test and verify the correctness and reliability of the proposed findings.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47803346","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 : 2022-04-20DOI: 10.15388/namc.2022.27.27326
Tingting Zhang, Jigui Jian
This article focuses on the global exponential synchronization (GES) for second-order state-dependent switched quaternion-valued neural networks (SOSDSQVNNs) with neutral-type and mixed delays. By proposing some new Lyapunov–Krasovskii functionals (LKFs) and adopting some inequalities, several new criteria in the shape of algebraic inequalities are proposed to ensure the GES for the concerned system by using hybrid switched controllers (HSCs). Different from the common reducing order and separation ways, this article presents some new LKFs to straightway discuss the GES of the concerned system based on non-reduction order and nonseparation strategies. Ultimately, an example is provided to validate the effectiveness of the theoretical outcomes.
{"title":"Exponential synchronization for second-order switched quaternion-valued neural networks with neutral-type and mixed time-varying delays","authors":"Tingting Zhang, Jigui Jian","doi":"10.15388/namc.2022.27.27326","DOIUrl":"https://doi.org/10.15388/namc.2022.27.27326","url":null,"abstract":"This article focuses on the global exponential synchronization (GES) for second-order state-dependent switched quaternion-valued neural networks (SOSDSQVNNs) with neutral-type and mixed delays. By proposing some new Lyapunov–Krasovskii functionals (LKFs) and adopting some inequalities, several new criteria in the shape of algebraic inequalities are proposed to ensure the GES for the concerned system by using hybrid switched controllers (HSCs). Different from the common reducing order and separation ways, this article presents some new LKFs to straightway discuss the GES of the concerned system based on non-reduction order and nonseparation strategies. Ultimately, an example is provided to validate the effectiveness of the theoretical outcomes.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48175260","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 : 2022-04-13DOI: 10.15388/namc.2022.27.26557
Lixiong Lin
In this paper, the fast synchronization problem of 5D Hindmarsh–Rose neuron networks is studied. Firstly, the global predefined-time stability of a class of nonlinear dynamical systems is investigated under the complete beta function. Then an active controller via backstepping design is proposed to achieve predefined-time synchronization of two 5D Hindmarsh–Rose neuron networks in which the synchronization time of each state variable of the master-slave 5D Hindmarsh–Rose neuron networks is different and can be defined in advance, respectively. To show the applicability of the obtained theoretical results, the designed predefined-time backstepping controller is applied to secure communication to realize asynchronous communication of multiple different messages. Three numerical simulations are provided to validate the theoretical results.
{"title":"Predefined-time synchronization of 5D Hindmarsh–Rose neuron networks via backstepping design and application in secure communication","authors":"Lixiong Lin","doi":"10.15388/namc.2022.27.26557","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26557","url":null,"abstract":"In this paper, the fast synchronization problem of 5D Hindmarsh–Rose neuron networks is studied. Firstly, the global predefined-time stability of a class of nonlinear dynamical systems is investigated under the complete beta function. Then an active controller via backstepping design is proposed to achieve predefined-time synchronization of two 5D Hindmarsh–Rose neuron networks in which the synchronization time of each state variable of the master-slave 5D Hindmarsh–Rose neuron networks is different and can be defined in advance, respectively. To show the applicability of the obtained theoretical results, the designed predefined-time backstepping controller is applied to secure communication to realize asynchronous communication of multiple different messages. Three numerical simulations are provided to validate the theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44063362","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 : 2022-04-13DOI: 10.15388/namc.2022.27.26741
S. Rajamani, A. Subramanyam Reddy
The current work deals with the pulsatile hydromagnetic flow of blood-based couple stress hybrid nanofluid in a porous channel. For hybrid nanofluid, the fusion of gold (Au) and copper oxide (CuO) nanoparticles are suspended to the blood (base fluid). In this model, the employment of viscous dissipation, radiative heat, and Ohmic heating is incorporated. The governing flow equations (set of partial differential equations) are modernized to set of ordinary differential equations by using the perturbation technique. The nondimensional governing equations are solved by adopting the shooting procedure with the help of the Runge–Kutta fourth-order approach. Temperature distributions of hybrid nanofluid and conventional mono nanofluids are portrayed via pictorial results to claim that the hybrid nanofluid has better temperature distribution than mono nanofluids. Temperature is raising for the magnifying viscous dissipation, whereas the reverse behavior can be found with a rise in couple stress parameter. The heat transfer rate is getting high for the higher values of the Eckert number, and the same behavior is noticed with the uplifting magnetic field.
{"title":"Effects of Joule heating, thermal radiation on MHD pulsating flow of a couple stress hybrid nanofluid in a permeable channel","authors":"S. Rajamani, A. Subramanyam Reddy","doi":"10.15388/namc.2022.27.26741","DOIUrl":"https://doi.org/10.15388/namc.2022.27.26741","url":null,"abstract":"The current work deals with the pulsatile hydromagnetic flow of blood-based couple stress hybrid nanofluid in a porous channel. For hybrid nanofluid, the fusion of gold (Au) and copper oxide (CuO) nanoparticles are suspended to the blood (base fluid). In this model, the employment of viscous dissipation, radiative heat, and Ohmic heating is incorporated. The governing flow equations (set of partial differential equations) are modernized to set of ordinary differential equations by using the perturbation technique. The nondimensional governing equations are solved by adopting the shooting procedure with the help of the Runge–Kutta fourth-order approach. Temperature distributions of hybrid nanofluid and conventional mono nanofluids are portrayed via pictorial results to claim that the hybrid nanofluid has better temperature distribution than mono nanofluids. Temperature is raising for the magnifying viscous dissipation, whereas the reverse behavior can be found with a rise in couple stress parameter. The heat transfer rate is getting high for the higher values of the Eckert number, and the same behavior is noticed with the uplifting magnetic field.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48089441","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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