Special Properties of Images and Corresponding Signals Generated by Chemical Reactions Discrete Chaotic Dynamics

Gontar, V.; Grechko, O.

doi:10.1142/s0218127407019147

Cited by 2 publications

(1 citation statement)

References 5 publications

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“…Instead of the arithmetic mean, we could consider a linear combination This can correspond to asymmetry of the environment (wind, water current etc. ); similar ideas for discrete chemical kinetics were developed in [19,20]. 5.…”

Section: Examples and Simulationsmentioning

confidence: 99%

Perturbations of a Spatial Ricker Model: Break of Chaos

Braverman¹,

Haroutunian²,

Cabada³

et al. 2009

AIP Conference Proceedings

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It is well known that as the intrinsic growth rate r increases, the Ricker map exhibits an irreversible period doubling route to chaos. If a constant positive perturbation is introduced, then there is a break of chaos giving birth to a two-cycle. We study a similar effect in a 2-dimensional spatial setting where each cell of the lattice is influenced by its nearest neighbours only. Chaos is not observed for r large enough, and the model can incorporate cells that experience two-cycle oscillations with stable dynamics at some locations. A Ricker map with a negative perturbation (depletion) is discussed, as well as some generalizations of the problem.where the right hand side is assumed to vanish if x"exp[r(l -x")] < d. This model was considered in [9] and on some general basis of Allee functions with a negative

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Section: Examples and Simulationsmentioning

confidence: 99%

Perturbations of a Spatial Ricker Model: Break of Chaos

Braverman¹,

Haroutunian²,

Cabada³

et al. 2009

AIP Conference Proceedings

View full text Add to dashboard Cite

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Chaotic and stable perturbed maps: 2-cycles and spatial models

Braverman

Haroutunian

2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

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As the growth rate parameter increases in the Ricker, logistic and some other maps, the models exhibit an irreversible period doubling route to chaos. If a constant positive perturbation is introduced, then the Ricker model (but not the classical logistic map) experiences period doubling reversals; the break of chaos finally gives birth to a stable two-cycle. We outline the maps which demonstrate a similar behavior and also study relevant discrete spatial models where the value in each cell at the next step is defined only by the values at the cell and its nearest neighbors. The stable 2-cycle in a scalar map does not necessarily imply 2-cyclic-type behavior in each cell for the spatial generalization of the map.

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Special Properties of Images and Corresponding Signals Generated by Chemical Reactions Discrete Chaotic Dynamics

Cited by 2 publications

References 5 publications

Perturbations of a Spatial Ricker Model: Break of Chaos

Perturbations of a Spatial Ricker Model: Break of Chaos

Chaotic and stable perturbed maps: 2-cycles and spatial models

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