Transition to coarse-grained order in coupled logistic maps: Effect of delay and asymmetry

Rajvaidya, Bhakti Parag; Deshmukh, Ankosh D.; Gade, Prashant M.; Sahasrabudhe, G. G.

doi:10.1016/j.chaos.2020.110301

Cited by 11 publications

(2 citation statements)

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“…An even greater variety of both spatial structures and dynamical regimes was obtained from studies of chains of globally coupled oscillators [13][14][15][16]. The main problem with this approach is that a large number of both parameters and ways of setting global couplings arise in such models, making it difficult to identify general patterns for systems of this kind.…”

Section: Discussionmentioning

confidence: 99%

“…Such a spatially distributed model allows for a large number of spatial structures and their associated effects [7,[10][11][12]. Recently, a number of studies describing the behavior of this class of models with different types of coupling (different depth of coupling, coupling with delay) have been conducted [13][14][15], and an attempt has been made to find universal regularities in the occurrence of spatial effects in a chain of diffusively coupled logistic oscillators [16]. Despite the abundance of various effects obtained in these models, no comparison of temporal dynamics and spatial structures has yet been made for a wide range of parameters.…”

Section: Introductionmentioning

confidence: 99%

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Emergent Spatial–Temporal Patterns in a Ring of Locally Coupled Population Oscillators

Rusakov,

Tikhonov,

Nurieva

et al. 2023

Mathematics

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A closed chain of oscillators can be considered a model for ring-shaped ecosystems, such as atolls or the coastal zones of inland reservoirs. We use the logistic map, which is often referred to as an archetypical example of how complex dynamics can arise from very simple nonlinear equations, as a model for a separate oscillator in the chain. We present an original algorithm that allows us to find solutions to the spatiotemporal logistic equation quite efficiently or to state with certainty that there are no such solutions. Based on the Shannon formula, we propose formulas for estimating the spatial and temporal entropy, which allow us to classify our solutions as regular or irregular. We show that regular solutions can occur within the Malthus parameter region that corresponds to the irregular dynamics of a solitary logistic map.

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Section: Discussionmentioning

confidence: 99%