Pub Date : 2023-05-01DOI: 10.1142/s0218127423300136
I. Bashkirtseva
In this paper, by the example of 3D model of enzyme reaction, we study mechanisms of noise-induced generation of complex multimodal chaotic oscillations in the monostability zone where only simple deterministic cycles are observed. In such a generation, a constructive role of deterministic toroidal transients is revealed. We perform a statistical analysis of these phenomena and localize the intensity range of the noise that causes stochastic [Formula: see text]- and [Formula: see text]-bifurcations connected with transitions to chaos and qualitative changes in the probability density. Constructive possibilities of the stochastic sensitivity function technique in the analytical study of these phenomena are demonstrated.
{"title":"Genesis of Noise-Induced Multimodal Chaotic Oscillations in Enzyme Kinetics: Stochastic Bifurcations and Sensitivity Analysis","authors":"I. Bashkirtseva","doi":"10.1142/s0218127423300136","DOIUrl":"https://doi.org/10.1142/s0218127423300136","url":null,"abstract":"In this paper, by the example of 3D model of enzyme reaction, we study mechanisms of noise-induced generation of complex multimodal chaotic oscillations in the monostability zone where only simple deterministic cycles are observed. In such a generation, a constructive role of deterministic toroidal transients is revealed. We perform a statistical analysis of these phenomena and localize the intensity range of the noise that causes stochastic [Formula: see text]- and [Formula: see text]-bifurcations connected with transitions to chaos and qualitative changes in the probability density. Constructive possibilities of the stochastic sensitivity function technique in the analytical study of these phenomena are demonstrated.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"15 1","pages":"2330013:1-2330013:9"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80793619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s0218127423500657
Doston Jumaniyozov, B. Omirov, Shovkat Redjepov, S. Uguz
In this paper, we consider a pentagonal lattice and we investigate the rule matrix with null boundary condition for two-dimensional cellular automata with the field [Formula: see text] (the set of integers modulo [Formula: see text]) and analyze their characteristics. Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained.
{"title":"Irreversibility of 2D Linear CA and Garden of Eden","authors":"Doston Jumaniyozov, B. Omirov, Shovkat Redjepov, S. Uguz","doi":"10.1142/s0218127423500657","DOIUrl":"https://doi.org/10.1142/s0218127423500657","url":null,"abstract":"In this paper, we consider a pentagonal lattice and we investigate the rule matrix with null boundary condition for two-dimensional cellular automata with the field [Formula: see text] (the set of integers modulo [Formula: see text]) and analyze their characteristics. Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"116 1","pages":"2350065:1-2350065:18"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79822303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s0218127423300148
Penghe Ge, Hongjun Cao
Neuroendocrine system mainly consists of hypothalamus, anterior pituitary, and target organ. In this paper, a three-state-variable delayed Goodwin model with two Hill functions is considered, where the Hill functions with delays denote the hormonal feedback suppressions from target organ to hypothalamus and to anterior in the reproductive hormonal axis. The existence of Hopf bifurcation shows the circadian rhythms of neuroendocrine system. The direction and stability of Hopf bifurcation are also analyzed using the normal form theory and the center manifold theorem for functional differential equations. Furthermore, based on the sparse identification algorithm, it is verified that the transient time series generated from the delayed Goodwin model cannot be equivalently presented by ordinary differential equations from the viewpoint of data when considering that a library of candidates are at most cubic terms. The reason is because the solution space of delayed differential equations is of infinite dimensions. Finally, we report that reservoir computing can predict the periodic behaviors of the delayed Goodwin model accurately if the size of reservoir and the length of data used for training are large enough. The predicting performances are evaluated by the mean squared errors between the trajectories generated from the numerical simulations and the reservoir computing.
{"title":"Dynamics of Delayed Neuroendocrine Systems and Their Reconstructions Using Sparse Identification and Reservoir Computing","authors":"Penghe Ge, Hongjun Cao","doi":"10.1142/s0218127423300148","DOIUrl":"https://doi.org/10.1142/s0218127423300148","url":null,"abstract":"Neuroendocrine system mainly consists of hypothalamus, anterior pituitary, and target organ. In this paper, a three-state-variable delayed Goodwin model with two Hill functions is considered, where the Hill functions with delays denote the hormonal feedback suppressions from target organ to hypothalamus and to anterior in the reproductive hormonal axis. The existence of Hopf bifurcation shows the circadian rhythms of neuroendocrine system. The direction and stability of Hopf bifurcation are also analyzed using the normal form theory and the center manifold theorem for functional differential equations. Furthermore, based on the sparse identification algorithm, it is verified that the transient time series generated from the delayed Goodwin model cannot be equivalently presented by ordinary differential equations from the viewpoint of data when considering that a library of candidates are at most cubic terms. The reason is because the solution space of delayed differential equations is of infinite dimensions. Finally, we report that reservoir computing can predict the periodic behaviors of the delayed Goodwin model accurately if the size of reservoir and the length of data used for training are large enough. The predicting performances are evaluated by the mean squared errors between the trajectories generated from the numerical simulations and the reservoir computing.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"66 1","pages":"2330014:1-2330014:23"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72866394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s0218127423500700
Mengdi Zhao, Hongjun Liu
The construction of multidimensional discrete hyperchaotic maps with ergodicity and larger Lyapunov exponents is desired in cryptography. Here, we have designed a general [Formula: see text]D ([Formula: see text]) discrete hyperchaotic map ([Formula: see text]D-DHCM) model that can generate any nondegenerate [Formula: see text]D chaotic map with Lyapunov exponents of desired size through setting the control matrix. To verify the effectiveness of the [Formula: see text]D-DHCM, we have provided two illustrative examples and analyzed their dynamic behavior, and the results demonstrated that their state points have ergodicity within a sufficiently large interval. Furthermore, to address the finite precision effect of the simulation platform, we analyzed the relationship between the size of Lyapunov exponent and the randomness of the corresponding state time sequence of the [Formula: see text]D-DHCM. Finally, we designed a keyed parallel hash function based on a 6D-DHCM to evaluate the practicability of the [Formula: see text]D-DHCM. Experimental results have demonstrated that [Formula: see text]D discrete chaotic maps constructed using [Formula: see text]D-DHCM have desirable Lyapunov exponents, and can be applied to practical applications.
{"title":"A Nondegenerate n-Dimensional Hyperchaotic Map Model with Application in a Keyed Parallel Hash Function","authors":"Mengdi Zhao, Hongjun Liu","doi":"10.1142/s0218127423500700","DOIUrl":"https://doi.org/10.1142/s0218127423500700","url":null,"abstract":"The construction of multidimensional discrete hyperchaotic maps with ergodicity and larger Lyapunov exponents is desired in cryptography. Here, we have designed a general [Formula: see text]D ([Formula: see text]) discrete hyperchaotic map ([Formula: see text]D-DHCM) model that can generate any nondegenerate [Formula: see text]D chaotic map with Lyapunov exponents of desired size through setting the control matrix. To verify the effectiveness of the [Formula: see text]D-DHCM, we have provided two illustrative examples and analyzed their dynamic behavior, and the results demonstrated that their state points have ergodicity within a sufficiently large interval. Furthermore, to address the finite precision effect of the simulation platform, we analyzed the relationship between the size of Lyapunov exponent and the randomness of the corresponding state time sequence of the [Formula: see text]D-DHCM. Finally, we designed a keyed parallel hash function based on a 6D-DHCM to evaluate the practicability of the [Formula: see text]D-DHCM. Experimental results have demonstrated that [Formula: see text]D discrete chaotic maps constructed using [Formula: see text]D-DHCM have desirable Lyapunov exponents, and can be applied to practical applications.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"1 1","pages":"2350070:1-2350070:16"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82312958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s021812742330015x
Shengjie Xu, Jing Ren, Musha Ji’e, Shukai Duan, Lidan Wang
The analysis of time series is essential in many fields, and reservoir computing (RC) can provide effective temporal processing that makes it well-suited for time series analysis and prediction tasks. In this study, we introduce a new discrete memristor model and a corresponding two-dimensional hyperchaotic map with complex dynamic properties that are well-suited for reservoir computing. By applying this map to the RC, we enhance the state richness of the reservoir, resulting in improved performance. The paper evaluates the performance of the proposed RC approach using time series data for sunspot, exchange rate, and solar-E forecasting tasks. Our experimental results demonstrate that this approach is highly effective in handling temporal data with both accuracy and efficiency. And comparing with other discrete memristive chaotic maps, the proposed map is the best for improving the RC performance. Furthermore, the proposed RC model is characterized by a simple structure that enables it to fully exploit the time-dependence of the state values of the hyperchaotic map.
{"title":"Application of Reservoir Computing Based on a 2D Hyperchaotic Discrete Memristive Map in Efficient Temporal Signal Processing","authors":"Shengjie Xu, Jing Ren, Musha Ji’e, Shukai Duan, Lidan Wang","doi":"10.1142/s021812742330015x","DOIUrl":"https://doi.org/10.1142/s021812742330015x","url":null,"abstract":"The analysis of time series is essential in many fields, and reservoir computing (RC) can provide effective temporal processing that makes it well-suited for time series analysis and prediction tasks. In this study, we introduce a new discrete memristor model and a corresponding two-dimensional hyperchaotic map with complex dynamic properties that are well-suited for reservoir computing. By applying this map to the RC, we enhance the state richness of the reservoir, resulting in improved performance. The paper evaluates the performance of the proposed RC approach using time series data for sunspot, exchange rate, and solar-E forecasting tasks. Our experimental results demonstrate that this approach is highly effective in handling temporal data with both accuracy and efficiency. And comparing with other discrete memristive chaotic maps, the proposed map is the best for improving the RC performance. Furthermore, the proposed RC model is characterized by a simple structure that enables it to fully exploit the time-dependence of the state values of the hyperchaotic map.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"151 1","pages":"2330015:1-2330015:16"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77769464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s0218127423500712
Xiao-Juan Liu, Xiao-Song Yang
In this paper, we study a family of planar piecewise linear systems with saddles separated by two parallel lines, and mainly investigate the existence of four-intersection-point limit cycles. We provide complete conclusions on the existence of a special four-intersection-point limit cycle and a heteroclinic loop. And, based on these results, we give some sufficient conditions for the existence of general four-intersection-point limit cycles. Some examples are given to illustrate the main results.
{"title":"Existence of Four-Intersection-Point Limit Cycles with Only Saddles Separated by Two Parallel Straight Lines in Planar Piecewise Linear Systems","authors":"Xiao-Juan Liu, Xiao-Song Yang","doi":"10.1142/s0218127423500712","DOIUrl":"https://doi.org/10.1142/s0218127423500712","url":null,"abstract":"In this paper, we study a family of planar piecewise linear systems with saddles separated by two parallel lines, and mainly investigate the existence of four-intersection-point limit cycles. We provide complete conclusions on the existence of a special four-intersection-point limit cycle and a heteroclinic loop. And, based on these results, we give some sufficient conditions for the existence of general four-intersection-point limit cycles. Some examples are given to illustrate the main results.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"16 1","pages":"2350071:1-2350071:16"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78680961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s0218127423500694
Bingxue Li, B. Sang, Mei Liu, Xiaoyan Hu, Xue Zhang, Ning Wang
Hidden chaotic attractors is a fascinating subject of study in the field of nonlinear dynamics. Jerk systems with a stable equilibrium may produce hidden chaotic attractors. This paper seeks to enhance our understanding of hidden chaotic dynamics in jerk systems of three variables [Formula: see text] with nonlinear terms from a predefined set: [Formula: see text], where [Formula: see text] is a real parameter. The behavior of the systems is analyzed using rigorous Hopf bifurcation analysis and numerical simulations, including phase portraits, bifurcation diagrams, Lyapunov spectra, and basins of attraction. For certain jerk systems with a subcritical Hopf bifurcation, adjusting the coefficient of a linear term can lead to hidden chaotic behavior. The adjustment modifies the subcritical Hopf equilibrium, transforming it from an unstable state to a stable one. One such jerk system, while maintaining its equilibrium stability, experiences a sudden transition from a point attractor to a stable limit cycle. The latter undergoes a period-doubling route to chaos, which may be followed by a reverse route. Therefore, by perturbing certain jerk systems with a subcritical Hopf equilibrium, we can gain insights into the formation of hidden chaotic attractors. Furthermore, adjusting the coefficient of the nonlinear term [Formula: see text] in certain systems with a stable equilibrium can also lead to period-doubling routes or reverse period-doubling routes to hidden chaotic dynamics. Both findings are significant for our understanding of the hidden chaotic dynamics that can emerge from nonlinear systems with a stable equilibrium.
{"title":"Some Jerk Systems with Hidden Chaotic Dynamics","authors":"Bingxue Li, B. Sang, Mei Liu, Xiaoyan Hu, Xue Zhang, Ning Wang","doi":"10.1142/s0218127423500694","DOIUrl":"https://doi.org/10.1142/s0218127423500694","url":null,"abstract":"Hidden chaotic attractors is a fascinating subject of study in the field of nonlinear dynamics. Jerk systems with a stable equilibrium may produce hidden chaotic attractors. This paper seeks to enhance our understanding of hidden chaotic dynamics in jerk systems of three variables [Formula: see text] with nonlinear terms from a predefined set: [Formula: see text], where [Formula: see text] is a real parameter. The behavior of the systems is analyzed using rigorous Hopf bifurcation analysis and numerical simulations, including phase portraits, bifurcation diagrams, Lyapunov spectra, and basins of attraction. For certain jerk systems with a subcritical Hopf bifurcation, adjusting the coefficient of a linear term can lead to hidden chaotic behavior. The adjustment modifies the subcritical Hopf equilibrium, transforming it from an unstable state to a stable one. One such jerk system, while maintaining its equilibrium stability, experiences a sudden transition from a point attractor to a stable limit cycle. The latter undergoes a period-doubling route to chaos, which may be followed by a reverse route. Therefore, by perturbing certain jerk systems with a subcritical Hopf equilibrium, we can gain insights into the formation of hidden chaotic attractors. Furthermore, adjusting the coefficient of the nonlinear term [Formula: see text] in certain systems with a stable equilibrium can also lead to period-doubling routes or reverse period-doubling routes to hidden chaotic dynamics. Both findings are significant for our understanding of the hidden chaotic dynamics that can emerge from nonlinear systems with a stable equilibrium.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"234 1","pages":"2350069:1-2350069:18"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72903770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s0218127423500682
Linping Peng, Yue Li, Dandi Sun
This paper studies the limit cycle bifurcations of a class of planar cubic isochronous centers. For different values of two key parameters, we give an estimate of the maximum number of limit cycles bifurcating from the period annulus of the unperturbed systems under arbitrarily small piecewise smooth polynomial perturbation. The main method and technique are based on the first order averaging theory for discontinuous systems and the Argument Principle in complex analysis.
{"title":"Piecewise Smooth Perturbations to a Class of Planar Cubic Centers","authors":"Linping Peng, Yue Li, Dandi Sun","doi":"10.1142/s0218127423500682","DOIUrl":"https://doi.org/10.1142/s0218127423500682","url":null,"abstract":"This paper studies the limit cycle bifurcations of a class of planar cubic isochronous centers. For different values of two key parameters, we give an estimate of the maximum number of limit cycles bifurcating from the period annulus of the unperturbed systems under arbitrarily small piecewise smooth polynomial perturbation. The main method and technique are based on the first order averaging theory for discontinuous systems and the Argument Principle in complex analysis.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"80 1","pages":"2350068:1-2350068:15"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74172174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s0218127423500761
Jing Su, Jiale Lu, Fan Sun, G. Zhou, Shukai Duan, Xiaofang Hu
Reservoir computing (RC) has attracted much attention as a brain-like neuromorphic computing algorithm for time series processing. In addition, the hardware implementation of the RC system can significantly reduce the computing time and effectively apply it to edge computing, showing a wide range of applications. However, many hardware implementations of RC use different hardware to implement standard RC without further expanding the RC architecture, which makes it challenging to deal with relatively complex time series tasks. Therefore, we propose a bidirectional hierarchical light reservoir computing method using optoelectronic memristors as the basis for the hardware implementation. The approach improves the performance of hardware-implemented RC by allowing the memristor to capture multilevel temporal information and generate a variety of reservoir states. Ag[Formula: see text]GQDs[Formula: see text]TiOx[Formula: see text]FTO memristors with negative photoconductivity effects can map temporal inputs nonlinearly to reservoir states and are used to build physical reservoirs to accomplish higher-speed operations. The method’s effectiveness is demonstrated in multivariate time series classification tasks: a predicted accuracy of 98.44[Formula: see text] is achieved in voiceprint recognition and 99.70[Formula: see text] in the mobile state recognition task. Our study offers a strategy for dealing with multivariate time series classification issues and paves the way to developing efficient neuromorphic computing.
{"title":"Efficient Neuromorphic Reservoir Computing Using Optoelectronic Memristors for Multivariate Time Series Classification","authors":"Jing Su, Jiale Lu, Fan Sun, G. Zhou, Shukai Duan, Xiaofang Hu","doi":"10.1142/s0218127423500761","DOIUrl":"https://doi.org/10.1142/s0218127423500761","url":null,"abstract":"Reservoir computing (RC) has attracted much attention as a brain-like neuromorphic computing algorithm for time series processing. In addition, the hardware implementation of the RC system can significantly reduce the computing time and effectively apply it to edge computing, showing a wide range of applications. However, many hardware implementations of RC use different hardware to implement standard RC without further expanding the RC architecture, which makes it challenging to deal with relatively complex time series tasks. Therefore, we propose a bidirectional hierarchical light reservoir computing method using optoelectronic memristors as the basis for the hardware implementation. The approach improves the performance of hardware-implemented RC by allowing the memristor to capture multilevel temporal information and generate a variety of reservoir states. Ag[Formula: see text]GQDs[Formula: see text]TiOx[Formula: see text]FTO memristors with negative photoconductivity effects can map temporal inputs nonlinearly to reservoir states and are used to build physical reservoirs to accomplish higher-speed operations. The method’s effectiveness is demonstrated in multivariate time series classification tasks: a predicted accuracy of 98.44[Formula: see text] is achieved in voiceprint recognition and 99.70[Formula: see text] in the mobile state recognition task. Our study offers a strategy for dealing with multivariate time series classification issues and paves the way to developing efficient neuromorphic computing.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"14 1","pages":"2350076:1-2350076:11"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79802027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-01DOI: 10.1142/s0218127423500748
Shangjiang Guo
We apply the [Formula: see text]-equivariant degree method to a Hopf bifurcation problem for functional differential equations with a state-dependent delay. The formal linearization of the system at a stationary state is extracted and translated into a bifurcation invariant by using the homotopy invariance of [Formula: see text]-equivariant degree. As a result, the local Hopf bifurcation is detected and the global continuation of periodic solutions is described.
{"title":"Global Hopf Bifurcation of State-Dependent Delay Differential Equations","authors":"Shangjiang Guo","doi":"10.1142/s0218127423500748","DOIUrl":"https://doi.org/10.1142/s0218127423500748","url":null,"abstract":"We apply the [Formula: see text]-equivariant degree method to a Hopf bifurcation problem for functional differential equations with a state-dependent delay. The formal linearization of the system at a stationary state is extracted and translated into a bifurcation invariant by using the homotopy invariance of [Formula: see text]-equivariant degree. As a result, the local Hopf bifurcation is detected and the global continuation of periodic solutions is described.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":" 635","pages":"2350074:1-2350074:13"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91409599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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