In-phase and anti-phase bursting dynamics and synchronisation scenario in neural network by varying coupling phase

Remi, T.; Subha, P. A.

doi:10.1007/s10867-023-09635-1

Cited by 3 publications

(1 citation statement)

References 68 publications

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“…With the help of the modified fast-slow decomposition analysis method, one can also analyze the mechanism of different bursting behaviors of high-dimensional system on different subplanes as well as the synchronization problems. In addition, as we know, bursting oscillations also have the other application scenarios, such as circuit parameter configurations [41,42], energy harvesting [43,44], spatiotemporal communications [45,46] and laser signal analysis [47,48]. In the future, the applications and control of the bursting patterns obtained in this paper will be investigated.…”

Section: Discussionmentioning

confidence: 78%

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Lyu,

Li,

Huang

et al. 2023

Phys. Scr.

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The study of bursting oscillations induced by frequency-domain multiscale effect is one of the key scientific issues in the theoretical analysis of circuit systems. In this paper, we explore the mechanism of the bursting oscillations of a van der Pol-Duffing-Jerk circuit oscillator with slow-changing parametric and external periodic excitations. Three typical bursting modes, namely, left-right symmetric “subHopf/fold limit cycle” bursting, origin symmetric “fold/fold limit cycle” bursting and origin symmetric “fold/subHopf/fold limit cycle” bursting, are presented. The slowly changing excitation is treated as a generalized state variable to analyze the influence on the critical manifolds of the equilibria and bifurcations. The critical conditions of fold and Hopf bifurcations are computed by using the bifurcation theory, and two typical bifurcation structures are obtained according to the position of different bifurcation curves. Based on the bifurcation analysis, we investigate the appearance and dynamicalal evolutions of the different bursting oscillations with the variation of the external excitation amplitude. It is pointed that not only the bifurcation structures but also the distance between the fold and Hopf bifurcation points can affect the bursting patterns. We find the directions of the trajectories and the bursting types are sensitive to the values of the external excitation amplitude. Furthermore, we reveal the mechanism of the bursting oscillations by overlapping the trajectories on (,x)-plane onto the corresponding bifurcation structures. Numerical simulations are also presented to prove the correctness of the theoretical analysis in our study.

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Section: Discussionmentioning

confidence: 78%

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Lyu,

Li,

Huang

et al. 2023

Phys. Scr.

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Dynamics and synchronization of the Morris-Lecar model with field coupling subject to electromagnetic excitation

Wei,

Li,

Zhang

2025

Communications in Nonlinear Science and Numerical Simulation

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Fixed Time Synchronization of Stochastic Takagi–Sugeno Fuzzy Recurrent Neural Networks with Distributed Delay under Feedback and Adaptive Controls

Niu,

Xu,

Liu

2024

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In this paper, the stochastic Takagi–Sugeno fuzzy recurrent neural networks (STSFRNNS) with distributed delay is established based on the Takagi–Sugeno (TS) model and the fixed time synchronization problem is investigated. In order to synchronize the networks, we design two kinds of controllers: a feedback controller and an adaptive controller. Then, we obtain the synchronization criteria in a fixed time by combining the Lyapunov method and the related inequality theory of the stochastic differential equation and calculate the stabilization time for the STSFRNNS. In addition, to verify the authenticity of the theoretical results, we use MATLABR2023A to carry out numerical simulation.

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In-phase and anti-phase bursting dynamics and synchronisation scenario in neural network by varying coupling phase

Abstract: Noname manuscript No.

Cited by 3 publications

References 68 publications

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Dynamics and synchronization of the Morris-Lecar model with field coupling subject to electromagnetic excitation

Fixed Time Synchronization of Stochastic Takagi–Sugeno Fuzzy Recurrent Neural Networks with Distributed Delay under Feedback and Adaptive Controls

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