Zero-Hopf bifurcation and multistability coexistence on a four-neuron network model with multiple delays

Ge, Juhong; Xu, Jian; Liu, Zhiqiang

doi:10.1007/s11071-016-3195-1

Cited by 13 publications

(3 citation statements)

References 34 publications

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“…( 31) yields the critical boundaries for the drilling stability, but this transcendental equation is unlike the one studied in [14] which has only an unique time delay. Equation (31) has n distinct delays, significantly complicating the calculation of eigenvalues, so the following analysis will employ numerical 140 iterations and continuation scheme [22] to obtain the critical boundaries.…”

Section: Stationary Drillingmentioning

confidence: 99%

Dynamics of rotary drilling with non-uniformly distributed blades

Yan

Wiercigroch

2019

International Journal of Mechanical Sciences

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Section: Stationary Drillingmentioning

confidence: 99%

Dynamics of rotary drilling with non-uniformly distributed blades

Yan

Wiercigroch

2019

International Journal of Mechanical Sciences

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“…Due to the complexity of global dynamics for all trajectories [27], there is very little research on multiple equilibria and their stability in low-dimensional nonlinear systems. In fact, the low-dimensional Hopfield neural system may exhibit the multi-coexistence of equilibria and periodic orbits [28,29]. Recently, Song et al [30] employed the multistage pitchfork bifurcations of trivial and nontrivial equilibrium to find the multiple coexistences of stable and unstable equilibria in the Wilson-Cowan coupled system, which is a global dynamical analysis.…”

Section: Introductionmentioning

confidence: 99%

Multiple bifurcations and periodic coexistence in a delayed Hopfield two-neural system with a monotonic activation function

et al. 2019

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In this paper, we consider a delayed Hopfield two-neural system with a monotonic activation function and find the periodic coexistence by bifurcation analysis. Firstly, we obtain the pitchfork bifurcation of the trivial equilibrium employing the central manifold and normal form methods. The neural system exhibits two pitchfork bifurcations near the trivial equilibrium. Then, analyzing the characteristic equation of the nontrivial equilibrium, we illustrate the saddle-node bifurcation of the nontrivial equilibria. The system exhibits the multi-coexistences of the stable and unstable equilibria. Further, we illustrate the plane regions of parameters having different numbers of equilibria. To obtain a time delay in neural system dynamics, we present the stability analysis and find the periodic orbit. The system exhibits stability switching by the Hopf bifurcation curves. Finally, the dynamic behaviors near the Hopf-Hopf bifurcation point are presented. The system exhibits coexistence of multiple periodic orbits with different frequencies.

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“…In addition to intermittency, time-delay systems are known to exhibit interesting dynamical features such as amplitude death [14,15], multistability [16] and quasiperiodicity [17]. In particular, recent theoretical [18] and experimental [19] studies have indicated various similarities between systems with long delays and spatio-temporal systems.…”

Section: Introductionmentioning

confidence: 99%

Intermittency in delay-coupled FitzHugh–Nagumo oscillators and loss of phase synchrony as its precursor

Saha¹,

Feudel²

2017

IASCS

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We study the dynamical properties of in-out intermittency in a system of two identical FitzHugh-Nagumo oscillators coupled by multiple time delays. In this system, the intermittency is manifested as irregular switching between a nearly synchronous state with small and large amplitude chaotic oscillations and a highly asynchronous state with a single large amplitude oscillation. We show that loss of phase synchrony significantly prior to the occurrence of the asynchronous large amplitude oscillation can be used as a precursor to the switching of states in such systems.

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Zero-Hopf bifurcation and multistability coexistence on a four-neuron network model with multiple delays

Cited by 13 publications

References 34 publications

Dynamics of rotary drilling with non-uniformly distributed blades

Dynamics of rotary drilling with non-uniformly distributed blades

Multiple bifurcations and periodic coexistence in a delayed Hopfield two-neural system with a monotonic activation function

Intermittency in delay-coupled FitzHugh–Nagumo oscillators and loss of phase synchrony as its precursor

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