Double time-delays induced stochastic dynamical characteristics for a metapopulation system subjected to the associated noises and a multiplicative periodic signal

In this article, synchronization inside complex networks with double time-delays and nonlinear inner-coupling functions are studied. Here double time-delays mean that each node vector field and every coupling node have retard time, while nonlinear inner-coupling functions refer to all the components of every node that are nonlinearly coupled. The theoretical criterion respecting synchronization is derived. And illustrative numerical examples are also given.

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Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Open Physics ◽

10.2478/s11534-009-0001-4 ◽

2009 ◽

Vol 7 (3) ◽

Cited By ~ 8

Author(s):

Chunyan Bai ◽

Luchun Du ◽

Dongcheng Mei

Keyword(s):

Stochastic Resonance ◽

Growth Model ◽

Noise Intensity ◽

Critical Phenomenon ◽

Fixed Ratio ◽

Logistic Growth ◽

Periodic Signal ◽

Logistic Growth Model ◽

Multiplicative Periodic Signal ◽

Correlated Noises

AbstractThe stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.

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Time delay effects of stochastic resonance induced by multiplicative periodic signal in the gene transcriptional regulatory model

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2018.05.025 ◽

2018 ◽

Vol 507 ◽

pp. 304-311 ◽

Cited By ~ 5

Author(s):

Chunyan Bai

Keyword(s):

Time Delay ◽

Stochastic Resonance ◽

Periodic Signal ◽

Transcriptional Regulatory ◽

Delay Effects ◽

Multiplicative Periodic Signal ◽

Regulatory Model

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Dynamics for the 3D incompressible Navier-Stokes equations with double time delays and damping

Discrete and Continuous Dynamical Systems - Series B ◽

10.3934/dcdsb.2021284 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Wei Shi ◽

Xiaona Cui ◽

Xuezhi Li ◽

Xin-Guang Yang

Keyword(s):

Time Delays ◽

Stokes Equations ◽

Three Dimensional ◽

Strong Solutions ◽

Navier Stokes ◽

Pullback Attractors ◽

Navier Stokes Equations ◽

Subcritical Nonlinearity ◽

Double Time ◽

Autonomous Dynamical Systems

<p style='text-indent:20px;'>This paper is concerned with the tempered pullback attractors for 3D incompressible Navier-Stokes model with a double time-delays and a damping term. The delays are in the convective term and external force, which originate from the control in engineer and application. Based on the existence of weak and strong solutions for three dimensional hydrodynamical model with subcritical nonlinearity, we proved the existence of minimal family for pullback attractors with respect to tempered universes for the non-autonomous dynamical systems.</p>

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