Global multistability and mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model

Gao, Chenghua; Qiao, Shuai; An, Xinlei

doi:10.1016/j.chaos.2022.112281

Cited by 17 publications

(3 citation statements)

References 82 publications

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“…With regard to the relevance of the occurrence of multistability in nonlinear dynamical systems, it is important to mention that the phenomenon has been recently reported in several other systems, among them neuron models [10,11], electronic circuits [12,13], memristor oscillators [14,15], biological systems [16,17], couplings of Duffing and van der Pol Oscillators [18], and snap and jerk systems [19,20], just to name a few among many examples.…”

Section: Discussionmentioning

confidence: 99%

Multistability in a Circulant Dynamical System

Rech

2023

Communications in Advanced Mathematical Sciences

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In this paper we report on a two parameter four-dimensional dynamical system with cyclic symmetry, namely a circulant dynamical system. This system is a twelve-term polynomial system with four cubic nonlinearities. Reported are some parameter-space diagrams for this system, all of them considering the same range of parameters, but generated from different initial conditions. We show that such diagrams display the occurrence of multistability in this system. Properly generated bifurcation diagrams confirm this finding. Basins of attraction of coexisting attractors in the related phase-space are presented, as well as an example showing phase portraits for periodic and chaotic coexisting attractors.

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Section: Discussionmentioning

confidence: 99%

Multistability in a Circulant Dynamical System

Rech

2023

Communications in Advanced Mathematical Sciences

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“…Hence our control measures here are reasonable and appropriate. Due to the fact that people tend to keep taking control measures for a while and the pest quantity would decrease continuously, it is found that the Filippov system is more suitable to describe pest control problems here, which is also applicable to other real-world issues [38][39]. Considering the carrying capacity of the predator, the Filippov system( 5) is proposed.…”

Section: Biological Implications and Conclusionmentioning

confidence: 99%

Dynamics of a non-smooth pest-natural enemy model with the threshold control strategy

2023

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Pest issues have always been the focus of attention in agriculture. The integrated Pest Management(IPM) method is currently the most popular way to be applied for pest control. In this study, according to the IPM strategy, we regard pest quantity as a threshold index and extend the Leslie-Gower model into a non-smooth Filippov system through combining chemical and biological control. To maintain the pest population at or below the given economic threshold(ET), we investigate the global dynamics of the proposed model, including the existence of sliding mode and various equilibria, sliding dynamics and bifurcations, and global stability of equilibria. The result shows that desired equilibria can be globally stable under some conditions, meaning that our control tactics work. In particular, the case where our strategy fails to be effective arouses interest. In the end, the biological implications of the results are discussed and given in detail.

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“…Karthikeyan et al [20] analyzed the effect of induced current on bifurcation patterns and spatiotemporal responses of the coupling network of a temperature-sensitive ML neuron. It is worth mentioning that memristors have important applications in stimulating multistability of continuous and non-smooth systems [21][22][23]. Besides, magnetic flux coupling plays a constructive role in realizing network synchronization and excitation of spiral waves [24,25].…”

Section: Introductionmentioning

confidence: 99%

Dynamics Analysis and Intermittent Energy Feedback Control of m‐HR Neuron Model under Electromagnetic Induction

Peng

2022

Complexity

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It is of great practical significance to fully reveal the global discharge characteristics of neurons in electromagnetic environment and design effective energy feedback strategy for accurate prediction of neural information. Considering the effect of electromagnetic induction, a four-dimensional modified Hindmarsh–Rose (m-HR) neuron model is established, and its discharge mechanism is revealed by analyzing the existence and stability of equilibrium point of the model. Extensive numerical results confirm that the model has classical period-doubling bifurcation, period-adding bifurcation, and comb-shaped chaotic structure. Importantly, a new intermittent energy feedback controller is designed by improving the traditional energy feedback control strategy, which can effectively modulate the desired discharge modes under the cost-optimal energy consumption. Meanwhile, it should be emphasized that the intermittent control scheme has a wider range of regulation and robustness, which can be applied to other dynamical systems to obtain the desired oscillation modes. This will improve the beneficial discussion for the construction of brain-like intelligent network and efficient regulation.

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Global multistability and mechanisms of a memristive autapse-based Filippov Hindmash-Rose neuron model

Cited by 17 publications

References 82 publications

Multistability in a Circulant Dynamical System

Multistability in a Circulant Dynamical System

Dynamics of a non-smooth pest-natural enemy model with the threshold control strategy

Dynamics Analysis and Intermittent Energy Feedback Control of m‐HR Neuron Model under Electromagnetic Induction

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