Chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process

Yang, Yi; Xiang, Changcheng; Dai, Xiaoyan; Zhang, Xianxiu; Qi, Liyuan; Zhu, Bin; Dong, Tao

doi:10.1007/s11571-021-09691-0

Cited by 4 publications

(2 citation statements)

References 49 publications

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“…In this case, other control measures such as spraying insecticides and manual capture need to be adopted together. In addition, this method of using the smooth Lyapunov function to prove the stability of nonsmooth systems can be extended to other nonsmooth ecosystems [22][23][24]. Some nonsmooth control systems can also be considered in the future [25][26][27][28][29].…”

Section: Conclusion Remarksmentioning

confidence: 99%

Stability for a Non-Smooth Filippov Ratio-Dependent Predator-Prey System through a Smooth Lyapunov Function

Yang

Dai

Zhang

et al. 2022

Mathematical Problems in Engineering

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For nonsmooth Filippov systems, the stability of the system is assumed to be proved by nonsmooth Lyapunov functions, such as piecewise smooth Lyapunov functions. This extension was based on the Filippov solution and Clarke generalized gradient. However, it is difficult to estimate the gradient of a non-smooth Lyapunov function. In some cases, the nonsmooth system can be divided into continuous and discontinuous components. If the Lebesgue measure of the discontinuous components is zero, the smooth Lyapunov function can be utilized to prove the stability of the system owing to the inner product of the gradient of the Lyapunov function of the discontinuous components being zero. In this paper, we apply the smooth Lyapunov function to prove the stability of the nonsmooth ratio-dependent predator-prey system. In contrast to the existing literature, in this paper, although the system is divided into continuous and discontinuous components, the inner product of the gradient of the Lyapunov function of the discontinuous part is not zero but negative. In the proof of stability, the negative value condition is stricter than the zero-value condition. This proof method only needs to construct a smooth Lyapunov function, which is simpler than a non-smooth Lyapunov function or other methods.

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Section: Conclusion Remarksmentioning

confidence: 99%

Stability for a Non-Smooth Filippov Ratio-Dependent Predator-Prey System through a Smooth Lyapunov Function

Yang

Dai

Zhang

et al. 2022

Mathematical Problems in Engineering

Self Cite

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“…Schuecker et al introduced the external signal in a manner of white noise to the neural network model, surprisingly finding a phase, neither chaotic nor linearly stable, maximizing the memory capacity of this network model (Schuecker et al, 2018). And some other computational neuroscientists investigated the influence of the random structures and stochastic perturbations positively or/and negatively on synchronization dynamics or computational behaviors in particularly coupled neural networks (Kim et al, 2020;Li et al, 2020;Pontes-Filho et al, 2020;Yang et al, 2022;Zhou et al, 2019;Leng and Aihara, 2020;Jiang and Lin, 2021).…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamics of Noise-Perturbed Excitatory-Inhibitory Neural Networks With Intra-Correlative and Inter-Independent Connections

Peng

Lin

2022

Front. Physiol.

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Real neural system usually contains two types of neurons, i.e., excitatory neurons and inhibitory ones. Analytical and numerical interpretation of dynamics induced by different types of interactions among the neurons of two types is beneficial to understanding those physiological functions of the brain. Here, we articulate a model of noise-perturbed random neural networks containing both excitatory and inhibitory (E&I) populations. Particularly, both intra-correlatively and inter-independently connected neurons in two populations are taken into account, which is different from the most existing E&I models only considering the independently-connected neurons. By employing the typical mean-field theory, we obtain an equivalent system of two dimensions with an input of stationary Gaussian process. Investigating the stationary autocorrelation functions along the obtained system, we analytically find the parameters’ conditions under which the synchronized behaviors between the two populations are sufficiently emergent. Taking the maximal Lyapunov exponent as an index, we also find different critical values of the coupling strength coefficients for the chaotic excitatory neurons and for the chaotic inhibitory ones. Interestingly, we reveal that the noise is able to suppress chaotic dynamics of the random neural networks having neurons in two populations, while an appropriate amount of correlation coefficient in intra-coupling strengths can enhance chaos occurrence. Finally, we also detect a previously-reported phenomenon where the parameters region corresponds to neither linearly stable nor chaotic dynamics; however, the size of the region area crucially depends on the populations’ parameters.

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Energy and synchronization between two neurons with nonlinear coupling

Guo,

Xie,

Wang

et al. 2023

Cogn Neurodyn

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Chimera states and cluster solutions in Hindmarsh-Rose neural networks with state resetting process

Cited by 4 publications

References 49 publications

Stability for a Non-Smooth Filippov Ratio-Dependent Predator-Prey System through a Smooth Lyapunov Function

Stability for a Non-Smooth Filippov Ratio-Dependent Predator-Prey System through a Smooth Lyapunov Function

Complex Dynamics of Noise-Perturbed Excitatory-Inhibitory Neural Networks With Intra-Correlative and Inter-Independent Connections

Energy and synchronization between two neurons with nonlinear coupling

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