Stability of multi-group models with cross-dispersal based on graph theory

Chen, Tianrui; Sun, Zhenyao; Wu, Boying

doi:10.1016/j.apm.2017.03.055

Cited by 18 publications

(7 citation statements)

References 25 publications

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“…In [43], a class of stochastic‐coupled oscillators as a practical application of the stochastic CSN without strong connectedness was investigated. Inspired by [41–43], the synchronisation of stochastic‐coupled oscillators with time‐varying delays and Lévy noise on networks without strong connectedness as an example of our abstract model is researched in this study.…”

Section: Application To Stochastic‐coupled Oscillators With Time‐vamentioning

confidence: 99%

Synchronisation of stochastic‐coupled intermittent control systems with delays and Lévy noise on networks without strong connectedness

Zhou

2019

IET Control Theory & Applications

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Section: Application To Stochastic‐coupled Oscillators With Time‐vamentioning

confidence: 99%

Synchronisation of stochastic‐coupled intermittent control systems with delays and Lévy noise on networks without strong connectedness

Zhou

2019

IET Control Theory & Applications

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“…On the other hand, dispersal is a common phenomenon in nature, which is due to the imbalance of oscillators in different regions. A lot of results about single dispersal have appeared in [ 8 â 10 ] since it plays an important role in the research of application problems. In addition, it is worth noting that dispersal also occurs between different oscillators of different groups, that is, bidirectional cross-dispersal.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Stability Analysis for Stochastic Coupled Oscillator Networks with Bidirectional Cross-Dispersal

Liu

Gao

2022

Computational Intelligence and Neuroscience

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It is well known that stochastic coupled oscillator network (SCON) has been widely applied; however, there are few studies on SCON with bidirectional cross-dispersal (SCONBC). This paper intends to study stochastic stability for SCONBC. A new and suitable Lyapunov function for SCONBC is constructed on the basis of Kirchhoff's matrix tree theorem in graph theory. Combining stochastic analysis skills and Lyapunov method, a sufficient criterion guaranteeing stochastic stability for the trivial solution of SCONBC is provided, which is associated with topological structure and coupling strength of SCONBC. Furthermore, some numerical simulation examples are given in order to illustrate the validity and practicability of our results.

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“…Hence, it is necessary to study the dynamics of the predator-prey model with cross-dispersal among all patches. Recently, cross-dispersal was used to study multi-group models (see [7]). Based on graph theory and Lyapunov functions method, the dynamics of a general multi-group model with cross-dispersal were given in [7].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, cross-dispersal was used to study multi-group models (see [7]). Based on graph theory and Lyapunov functions method, the dynamics of a general multi-group model with cross-dispersal were given in [7]. To the best of the author's knowledge, few researchers have focused on the dynamics of predator-prey models with cross-dispersal.…”

Section: Introductionmentioning

confidence: 99%

Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory

Gao

2021

Adv Differ Equ

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In this paper, cross-dispersal is considered in a predator–prey model with a patchy environment. A new predator–prey model with cross-dispersal among patches is constructed. A new cross-dispersal matrix is established by the coupling relationship between vertices. First, an existence theorem of the positive equilibrium for the new model is obtained. Secondly, based on the idea of constructing Lyapunov functions and a graph-theoretical approach for coupled systems, sufficient conditions that the positive equilibrium of the new model is globally asymptotically stable in $R^{2n}_{+}$ R + 2 n are derived on a network with strongly connected graphs. Thirdly, based on the theory of asymptotically autonomous systems, Lyapunov functions method and graph theory, a stability theorem for the positive equilibrium of the new model is established on a complex network without strongly connected graphs. Finally, two examples are given to illustrate main results.

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Stability of multi-group models with cross-dispersal based on graph theory

Cited by 18 publications

References 25 publications

Synchronisation of stochastic‐coupled intermittent control systems with delays and Lévy noise on networks without strong connectedness

Synchronisation of stochastic‐coupled intermittent control systems with delays and Lévy noise on networks without strong connectedness

Stochastic Stability Analysis for Stochastic Coupled Oscillator Networks with Bidirectional Cross-Dispersal

Global stability for a new predator–prey model with cross-dispersal among patches based on graph theory

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