Snap-back repellers and chaos in a discrete population model with delayed recruitment

Morris, Hedley C.; Ryan, E.E.; Dodd, R. K.

doi:10.1016/0362-546x(83)90046-9

Cited by 16 publications

(2 citation statements)

References 20 publications

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“…So, although non-smooth systems are widespread in engineering [33,34], economics [35], ecology [36,37] and biology [38,39], the exploration of such systems under coupling in wide ranging topologies has been limited.…”

Section: Introductionmentioning

confidence: 99%

Effect of switching links in networks of piecewise linear maps

Sinha

2015

Nonlinear Dyn

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We investigate the spatiotemporal behaviour of a network where the local dynamics at the nodes (sites) is governed by piecewise linear maps. The local maps we consider exhibit the interesting and potentially useful property of robust chaos. We study the coupled system of such maps with varying fraction of random non-local connections, where the random links may be static, or may change over time. While this system is always unsynchronized under regular connections, synchronized chaos emerges when some of the links are rewired randomly. Further, increasing the frequency of link changes and fraction of random links significantly enhances the range of synchronization. Additionally, dynamic random links are also found to suppress unbounded dynamics in parameter regimes where blow-ups occurred under regular coupling.

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Section: Introductionmentioning

confidence: 99%

Effect of switching links in networks of piecewise linear maps

Sinha

2015

Nonlinear Dyn

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“…It is the case in some control systems using either sampled data, or switching elements, or pulse modulation, and also in some adaptive controls [Mira & Roubellat, 1969;Gumowski & Mira, 1980;Cathala, 1982a;Mira, 1990;Adomaitis & Kevrekidis, 1991;Frouzakis et al, 1992;Adomaitis et al, 1992]. Moreover, modeling in economics [Delli Gatti et al, 1993;Gardini, 1993], ecology and biology [Morris et al, 1983a[Morris et al, , 1983bMay, 1974May, , 1976Beddington et al, 1975;May & Oster, 1976;Clerc et al, 1977;Guckenheimer et al, 1977] gives rise to noninvertible maps.…”

Section: Introductionmentioning

confidence: 99%

Fractalization of Basin Boundary in Two-Dimensional Noninvertible Maps

Cathala

1999

Int. J. Bifurcation Chaos

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Properties of the basins of a two-dimensional noninvertible degenerated map is studied using the method of critical curves. More precisely, this paper considers a cubic map that belongs to the class of maps having the plane subdivided by the branches of the critical curve in three regions, two nonconnected with one preimage, the other with three distinct preimages. The fractalization of the basin of such an endomorphism is described.

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Dynamical Behaviors in a Two-dimensional Map

Chang

2003

Acta Mathematicae Applicatae Sinica, English Series

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Snap-back repellers and chaos in a discrete population model with delayed recruitment

Cited by 16 publications

References 20 publications

Effect of switching links in networks of piecewise linear maps

Effect of switching links in networks of piecewise linear maps

Fractalization of Basin Boundary in Two-Dimensional Noninvertible Maps

Dynamical Behaviors in a Two-dimensional Map

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