Stability and bifurcation analysis of an annular delayed neural network with self-connection

Yuan, Shaoliang; Li, Xuemei

doi:10.1016/j.neucom.2010.08.010

Cited by 12 publications

(2 citation statements)

References 24 publications

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“…Zhu and Huang considered a static recurrent network model with delayed neural feedback and neural interaction history. Nevertheless, in together with , the time delay in the leakage term has been ignored. Further, up to now, to the best of our knowledge, few results on the bifurcation of neural network with time delay in the leakage term have been obtained.…”

Section: Direction and Stability Of Hopf Bifurcationmentioning

confidence: 99%

“…As pointed out by Gopalsamy , time delay in the stabilizing negative feedback term has a tendency to destabilize a system. On the other hand, although the constant discrete delays in neural network models provide a good approximation describing the delayed feedbacks and are studied extensively (for example, and references therein), neural networks usually have a spatial extent due to presence of a multitude of parallel pathways with a variety of axon sizes and lengths; hence, there is a distribution of propagation delays over a period. In this case, the signal propagation is no longer instantaneous and cannot be modeled with discrete time delay only.…”

Section: Introductionmentioning

confidence: 99%

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Stability and bifurcation analysis for a neural network model with discrete and distributed delays

Liu

2012

Math Methods in App Sciences

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In this paper, a two-neuron network with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the trivial equilibrium is investigated. With the discrete time delay taken as a bifurcation parameter, the existence of Hopf bifurcation is established. Moreover, formulae for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate the main results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics.

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Section: Direction and Stability Of Hopf Bifurcationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis for a neural network model with discrete and distributed delays

Liu

2012

Math Methods in App Sciences

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Dynamics of unidirectionally-coupled ring neural network with discrete and distributed delays

2020

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Bifurcation Behavior for an Electronic Neural Network Model with Two Different Delays

Shao

2014

Neural Process Lett

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In this paper, an electronic neural network model with two different delays is investigated. The conditions for the local stability and the existence of Hopf bifurcation at the equilibrium of the system are derived. By applying the normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are obtained. Numerical simulations for justifying the theoretical analysis are also included. Finally, main conclusions are given.

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Stability and bifurcation analysis of an annular delayed neural network with self-connection

Cited by 12 publications

References 24 publications

Stability and bifurcation analysis for a neural network model with discrete and distributed delays

Stability and bifurcation analysis for a neural network model with discrete and distributed delays

Dynamics of unidirectionally-coupled ring neural network with discrete and distributed delays

Bifurcation Behavior for an Electronic Neural Network Model with Two Different Delays

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