Self-/mutual-symmetric rhythms and their coexistence in a delayed half-center oscillator of the CPG neural system

Song, Zigen; Xu, Jian

doi:10.1007/s11071-022-07222-y

Cited by 30 publications

(8 citation statements)

References 39 publications

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“…Ecological system is a singularly complicated spatiotemporal composite dynamic system. Many scholars considered the effect of delay, 35,36,39–41 and it is interesting to study the predator–prey system with one delay or multiple delays. Moreover, for system (), the effects of time‐delay or reaction‐diffusion have been extensively studied 24,42–45 .…”

Section: Discussionmentioning

confidence: 99%

Bifurcation analysis of a predator–prey model with Beddington–DeAngelis functional response and predator competition

Zhang

Huang

2022

Math Methods in App Sciences

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In this paper, we consider a predator-prey model with Beddington-DeAngelis functional response and predator competition, which is a five-parameter family of planar vector field. It is shown that the model can undergo a sequence of bifurcations including focus type degenerate Bogdanov-Takens bifurcation of codimension 3 and Hopf bifurcation of codimension at least 2 as the parameters vary. Our theoretical results indicate that predator competition can cause richer dynamics such as two limit cycles enclosing one or three hyperbolic positive equilibria and three kinds of homoclinic orbits (homoclinic to hyperbolic saddle, saddle-node, or neutral saddle). Moreover, there exists a threshold value m 0 for predator capturing rate m, below or equal to which the predators always tend to extinction, above which the predators and preys will coexist in the form of multiple steady states or periodic oscillations for all positive initial populations.Numerical simulations are presented to illustrate the theoretical results.

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Section: Discussionmentioning

confidence: 99%

Bifurcation analysis of a predator–prey model with Beddington–DeAngelis functional response and predator competition

Zhang

Huang

2022

Math Methods in App Sciences

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“…Based on our previous article (Song and Xu, 2022), the delayed HCO neural system (2) always presents the trivial equilibrium (0, 0, 0, 0) for arbitrary values of the system parameters. Further, the nontrivial equilibrium can be obtained by a static bifurcation of the trivial equilibrium.…”

Section: The Delayed Hco Modelmentioning

confidence: 96%

“…The delayed-HCO (DHCO) system consisting of two inertial neurons is presented by the following delay differential equation (DDE), which is (Song and Xu, 2022)…”

Section: The Delayed Hco Modelmentioning

confidence: 99%

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Multiple Switching and Bifurcations of In-phase and Anti-phase Periodic Orbits to Chaos Coexistence in a Delayed Half-center CPG Oscillator

Song

2023

Preprint

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In this study, we investigate complex dynamical behaviors of a delayed HCO (half-center oscillator) neural system consisted of two inertial neurons. The neural system proposes two types of periodic orbits with in-phase and anti-phase spatiotemporal patterns that arise via the Hopf bifurcation of the trivial equilibrium and the homoclinic orbit (Homo) bifurcation of the nontrivial equilibrium. With increasing time delay, the periodic orbit translates into a quasi-periodic orbit and enters chaos attractor by employing the quasi-periodic orbit bifurcation. Further, the chaos attractor breaks and bifurcates into a pair of symmetry multiple-periodic orbits, which evolves into a pair of symmetry chaos attractors by the period-doubling bifurcation. The delayed HCO neural system presents multiple coexistence employing two classical bifurcation routes to chaos, i.e. the quasi-periodic orbit and period-doubling bifurcations. What is interesting is that the delayed HCO neural system proposes seven similar sequences (maybe up to infinity) of the bifurcation routes to chaos with the increasing of the variable bifurcation parameter τ. In the presented paper, we just exhibit 14 attractors’ coexistence induced by the multiple bifurcation routes, which includes periodic orbits, quasi-periodic orbits, chaos attractors, and multiple-periodic orbits.

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“…In fact, HCO (half-center oscillator) is a basic and pivotal motif in biological CPG system [35,36]. In our previous paper, we have proposed the DHCO (delayed half-center oscillator) neural system and analyzed the symmetric patterns of rhythm activity [37]. The DHCO system presents many types of rhythm activities with self-and mutual-symmetric patterns by different bifurcation mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal pattern of periodic rhythms in delayed Van der Pol oscillators for the CPG-based locomotion of snake-like robot

Song

Huang

2022

Nonlinear Dyn

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Self-/mutual-symmetric rhythms and their coexistence in a delayed half-center oscillator of the CPG neural system

Cited by 30 publications

References 39 publications

Bifurcation analysis of a predator–prey model with Beddington–DeAngelis functional response and predator competition

Bifurcation analysis of a predator–prey model with Beddington–DeAngelis functional response and predator competition

Multiple Switching and Bifurcations of In-phase and Anti-phase Periodic Orbits to Chaos Coexistence in a Delayed Half-center CPG Oscillator

Spatiotemporal pattern of periodic rhythms in delayed Van der Pol oscillators for the CPG-based locomotion of snake-like robot

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