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Coexisting multi-period and chaotic attractor in fully connected system via adaptive multi-body interaction control

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Abstract

Multi-body interaction has been proved to exist widely in the real world. To verify the influence of multi-body interactive feedback on the dynamics of system, a novel adaptive time-delay multi-body interaction control is proposed in this work. The global stability and local bifurcation of the controlled system are investigated. Applying the controller to ternary and quaternary neural network models, we find that there are complex dynamical phenomena in the controlled networks. When the time delay is small, only a single asymptotically stable solution is observed. With the increase in the time delay, the system undergoes a periodic solution induced by Hopf bifurcation. However, with further increase in the time delay, multi-periodic solutions and multiple chaotic attractors coexist near the equilibrium point. Compared with the traditional controller, the adaptive multi-body feedback controller can make the neural network system without non-trivial phenomenon enable complex coexistence phenomenon, only by controlling one neuron node.

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Acknowledgements

The author is grateful to all anonymous reviewers for their valuable comments, which has provided great help for the improvement of the paper.

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  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Qinrui Dai

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  1. Qinrui Dai
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Dai, Q. Coexisting multi-period and chaotic attractor in fully connected system via adaptive multi-body interaction control. Nonlinear Dyn 112, 681–692 (2024). https://doi.org/10.1007/s11071-023-09061-x

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