Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

Ma, Jinzhong; Xu, Yong; Li, Yongge; Tian, Ruilan; Ma, Shuping; Kurths, Jürgen

doi:10.1007/s10483-021-2672-8

Cited by 32 publications

(13 citation statements)

References 33 publications

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“…It is well known that the neurons link each other through a network, and the brain activity is the collective behavior of the neurons rather than a single neuron. Pattern formation and bifurcation Tian et al (2021) ; Yang (2022) ; Ma et al (2021) is a crucial tool to elaborate on the dynamic and biological mechanism of the collective behavior of the neurons. In this paper, an HR model with a random network is considered to show the spatiotemporal patterns of collective behaviors.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model

et al. 2022

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Neuron modelling helps to understand the brain behavior through the interaction between neurons, but its mechanism remains unclear. In this paper, the spatiotemporal patterns is investigated in a general networked Hindmarsh-Rose (HR) model. The stability of the network-organized system without delay is analyzed to show the effect of the network on Turing instability through the Hurwitz criterion, and the conditions of Turing instability are obtained. Once the analysis of the zero-delayed system is completed, the critical value of the delay is derived to illustrate the profound impact of the given network on the collected behaviors. It is found that the difference between the collected current and the outgoing current plays a crucial role in neuronal activity, which can be used to explain the generation mechanism of the short-term memory. Finally, the numerical simulation is presented to verify the proposed theoretical results.

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Section: Introductionmentioning

confidence: 99%

Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model

et al. 2022

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“…However, excitations in practical applications are not always continuous, and random discontinuous excitations have been observed in practice 19–23 . The existence of stochastic jumps causes discontinuous changes in system states, which cannot be characterized by continuous excitations.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of an SDOF quasi‐linear system with jump noises and multitime‐delayed feedback forces

Jia

Luo

Hao

et al. 2022

Int Journal of Mech Sys Dyn

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In this paper, stochastic dynamics of a single degree-of-freedom quasi-linear system with multitime delays and Poisson white noises are investigated using an approximate procedure based on the stochastic averaging method. The simplified equations, including the averaged stochastic differential equation and the averaged generalized Fokker-Planck-Kolmogorov equation, are obtained to calculate the probability density functions (PDFs) to explore stationary responses.The expression of the Lyapunov exponent is presented to examine the asymptotic stochastic Lyapunov stability. An illustrative example of a quasi-linear oscillator with two Poisson white noises controlled by two time-delayed feedback forces is worked out to demonstrate the validity of the proposed method. The approximate stationary PDFs of stochastic responses and asymptotic stochastic stability are demonstrated numerically and theoretically. The results show that the Gaussian white noise has a stronger influence on the dynamics than the Poisson white noise with a small mean arrival rate. Moreover, the influence of the time delay and noise parameters on stochastic dynamics is investigated. It is found that the PDFs under the Poisson white noise approach those under Gaussian white noise as the mean arrival rate increases. The time delay can induce stochastic P-bifurcation of the system. It is also found that the increase of time delay and the mean arrival rates of the Poisson white noises will broaden the unstable parameter region. The comparison between numerical and theoretical results shows the effectiveness of the proposed method.time delay, stochastic response and stability, Poisson white noise | INTRODUCTIONTime delay can be experienced in many applications and fields, such as power, electronic technology, network, and transportation systems. The existence of time delay significantly affects the system behavior, especially for enormous nonlinear engineering structures. 1-3 For example, time delay in feedback control systems cannot be avoided because it takes time to detect the system state, calculate the control force, and transfer the control signal from the computer to the actuator. Time delay does not only affect the control effect but can cause

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“…Many studies try to indicate bifurcation points [53,54]. Prediction of noise-induced critical transitions was studied in [55]. e most exciting predictors of bifurcation points are autocorrelation at lag-1 and variance [47].…”

Section: Introductionmentioning

confidence: 99%

Predicting Tipping Points in Chaotic Maps with Period‐Doubling Bifurcations

Ramesh

Rajagopal

et al. 2021

Complexity

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In this paper, bifurcation points of two chaotic maps are studied: symmetric sine map and Gaussian map. Investigating the properties of these maps shows that they have a variety of dynamical solutions by changing the bifurcation parameter. Sine map has symmetry with respect to the origin, which causes multistability in its dynamics. The systems’ bifurcation diagrams show various dynamics and bifurcation points. Predicting bifurcation points of dynamical systems is vital. Any bifurcation can cause a huge wanted/unwanted change in the states of a system. Thus, their predictions are essential in order to be prepared for the changes. Here, the systems’ bifurcations are studied using three indicators of critical slowing down: modified autocorrelation method, modified variance method, and Lyapunov exponent. The results present the efficiency of these indicators in predicting bifurcation points.

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Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

Cited by 32 publications

References 33 publications

Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model

Spatiotemporal Patterns in a General Networked Hindmarsh-Rose Model

Dynamical analysis of an SDOF quasi‐linear system with jump noises and multitime‐delayed feedback forces

Predicting Tipping Points in Chaotic Maps with Period‐Doubling Bifurcations

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