Simple estimation of synchronization threshold in ensembles of diffusively coupled chaotic systems

Stefański, Andrzej; Wojewoda, Jerzy; Kapitaniak, Tomasz; Yanchuk, Serhiy

doi:10.1103/physreve.70.026217

Cited by 26 publications

(9 citation statements)

References 25 publications

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“…In the examples shown in both figures 9 and 10, the diffusion was increased in order to regularize the respective Turing or Benjamin–Feir instability. Large enough coupling strengths (in our case, diffusion parameters) have been shown to synchronize oscillator systems in the literature [62,63], hence our results suggest that a similar dependence holds in the non-autonomous setting.…”

Section: Control and Prevention Of Patterns On Networksupporting

confidence: 66%

A theory of pattern formation for reaction–diffusion systems on temporal networks

Gorder

2021

Proc. R. Soc. A.

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Networks have become ubiquitous in the modern scientific literature, with recent work directed at understanding ‘temporal networks’—those networks having structure or topology which evolves over time. One area of active interest is pattern formation from reaction–diffusion systems, which themselves evolve over temporal networks. We derive analytical conditions for the onset of diffusive spatial and spatio-temporal pattern formation on undirected temporal networks through the Turing and Benjamin–Feir mechanisms, with the resulting pattern selection process depending strongly on the evolution of both global diffusion rates and the local structure of the underlying network. Both instability criteria are then extended to the case where the reaction–diffusion system is non-autonomous, which allows us to study pattern formation from time-varying base states. The theory we present is illustrated through a variety of numerical simulations which highlight the role of the time evolution of network topology, diffusion mechanisms and non-autonomous reaction kinetics on pattern formation or suppression. A fundamental finding is that Turing and Benjamin–Feir instabilities are generically transient rather than eternal, with dynamics on temporal networks able to transition between distinct patterns or spatio-temporal states. One may exploit this feature to generate new patterns, or even suppress undesirable patterns, over a given time interval.

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Section: Control and Prevention Of Patterns On Networksupporting

confidence: 66%

A theory of pattern formation for reaction–diffusion systems on temporal networks

Gorder

2021

Proc. R. Soc. A.

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“…We illustrate the implementation of the proposed conditions for stochastic synchronization through the analysis of canonical Henon maps coupled through the pristine network defined above. The chaotic dynamics of each individual map is governed by [35,56] x…”

Section: B Illustration Of the Methodsmentioning

confidence: 99%

“…are the eigenvalues of L 0 ordered in nondecreasing order with η 1 = 0 corresponding to the eigenvector 1 N , see also [56]. Therefore, (14) reduces to the classical stability result for static networks of coupled maps [53][54][55][56], that is,…”

Section: Master Equationmentioning

confidence: 98%

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Stochastic synchronization in blinking networks of chaotic maps

Porfiri

2012

Phys. Rev. E

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In this paper we analyze stochastic synchronization of coupled chaotic maps over blinking networks composed of a pristine static network and stochastic on-off couplings between any pair of nodes. We focus on mean square linear stability of the synchronized state by analyzing the time evolution of the second moment of the variation transverse to the synchronization manifold. By projecting the variational equations on the eigenvectors of a higher order state matrix describing this variational dynamics, we establish a necessary and sufficient condition for stochastic synchronization based on the largest Lyapunov exponent of the map and the spectral radius of such matrix. This condition is further simplified by computing closed-form results for the spectral properties of the moments of the graph Laplacian associated to the intermittent coupling and using classical eigenvalue bounds. We illustrate the main results through simulations on synchronization of chaotic Henon maps.

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“…According to Refs. [12,[29][30][31], around the synchronized states s n , the variational equations of Eq. ( 6) can be written as…”

Section: Analysing the Largest Lyapunov Exponents Of The Systemmentioning

confidence: 99%

Synchronization of coupled logistic maps on random community networks

Feng¹,

Xu²,

Wu³

et al. 2008

Chinese Phys. B

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The collective synchronization of a system of coupled logistic maps on random community networks is investigated. It is found that the synchronizability of the community network is affected by two factors when the size of the network and the number of connections are fixed. One is the number of communities denoted by the parameter m, and the other is the ratio σ of the connection probability p of each pair of nodes within each community to the connection probability q of each pair of nodes among different communities. Theoretical analysis and numerical results indicate that larger m and smaller σ are the key to the enhancement of network synchronizability. We also testify synchronous properties of the system by analysing the largest Lyapunov exponents of the system.

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Simple estimation of synchronization threshold in ensembles of diffusively coupled chaotic systems

Cited by 26 publications

References 25 publications

A theory of pattern formation for reaction–diffusion systems on temporal networks

A theory of pattern formation for reaction–diffusion systems on temporal networks

Stochastic synchronization in blinking networks of chaotic maps

Synchronization of coupled logistic maps on random community networks

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