Spatially periodic orbits in coupled-map lattices

Gade, Prashant M.; Amritkar, R. E.

doi:10.1103/physreve.47.143

Cited by 49 publications

(39 citation statements)

References 17 publications

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“…However, periodic orbit arguments have been used to justify thermodynamic results such as non-negativity of the entropy production [27] and the Onsager relations [28] without explicitly finding any periodic orbits. Periodic orbits of spatially extended systems in the form of coupled map lattices have been considered previously [29,30], leading to block cyclic matrices similar to those observed in this paper.…”

Section: Introductionsupporting

confidence: 70%

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Taniguchi

Dettmann

Morriss

2002

Journal of Statistical Physics

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The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional many particle system with hard core interactions is discussed. Noting that the matrix to describe the tangent space dynamics has the block cyclic structure, the calculation of the Lyapunov spectrum is attributed to the eigenvalue problem of 16 × 16 reduced matrices regardless of the number of particles. We show that there is the thermodynamic limit of the Lyapunov spectrum in this periodic orbit. The Lyapunov spectrum has a step structure, which is explained by using symmetries of the reduced matrices.

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Section: Introductionsupporting

confidence: 70%

“…[30] to reduce the problem of computing the Lyapunov spectrum to that of finding the eigenvalues of a relatively small (16 × 16) matrix. A step structure is observed, which is related to the symmetries of the system.…”

Section: Introductionmentioning

confidence: 99%

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Taniguchi

Dettmann

Morriss

2002

Journal of Statistical Physics

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“…An important model of this kind is the coupled map lattice, which has also often been studied for reasons independent of its ecological significance (Amritkar et al, 1991;Amritkar and Gade, 1993;Anteneodo et al, 2003;Astakhov et al, 1995;Gade and Amritkar, 1993;Kaneko, 1992aKaneko, , 1992bKaneko, , 1993Konishi and Kaneko, 1992;Lai, 1995;Manrubia and Mikhailov, 2000;Morita, 1996;Parekh et al, 1998;Silva et al, 2001;Zhu et al, 2003;De Monte et al, 2004;Lai, 1995). For ecological models of this type, a particular map governs the local dynamics at some number of discrete locations, and the populations at each location are connected to nearby locations according to some dispersal rule.…”

Section: General Backgroundmentioning

confidence: 99%

Sudden Shifts in Ecological Systems: Intermittency and Transients in the Coupled Ricker Population Model

Wysham

Hastings

2007

Bull. Math. Biol.

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Many real ecological systems show sudden changes in behavior, phenomena sometimes categorized as regime shifts in the literature. The relative importance of exogenous versus endogenous forces producing regime shifts is an important question. These forces' role in generating variability over time in ecological systems has been explored using tools from dynamical systems. We use similar ideas to look at transients in simple ecological models as a way of understanding regime shifts. Based in part on the theory of crises, we carefully analyze a simple two patch spatial model and begin to understand from a mathematical point of view what produces transient behavior in ecological systems. In particular, since the tools are essentially qualitative, we are able to suggest that transient behavior should be ubiquitous in systems with overcompensatory local dynamics, and thus should be typical of many ecological systems.

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“…The following represents a generalization of the linear stability analysis that has been carried out in the literature for some special cases such as global coupling [12], nearest neighbor coupling [13], and random coupling [14].…”

Section: CML and Its Spectrummentioning

confidence: 99%

Spectral properties and synchronization in coupled map lattices

2001

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Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The quadratic map is used for the site dynamics with different coupling schemes such as global coupling, nearest neighbor coupling, intermediate range coupling, random coupling, small world coupling and scale free coupling.

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Spatially periodic orbits in coupled-map lattices

Cited by 49 publications

References 17 publications

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Sudden Shifts in Ecological Systems: Intermittency and Transients in the Coupled Ricker Population Model

Spectral properties and synchronization in coupled map lattices

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