Models of coupled population oscillators using 1-D maps

Vandermeer, John; Kaufmann, Andrew M.

doi:10.1007/s002850050125

Cited by 9 publications

(2 citation statements)

References 24 publications

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“…This effect occurs to be a result of closeness of the chaotic dynamics of the response system to a periodic window [24]. As applied to ecological systems, it has been shown theoretically that coupling between two habitats can cause chaotic populations to behave non-chaotically [25][26][27].…”

Section: Discussionmentioning

confidence: 99%

Emergence of Self-Organized Dynamical Domains in a Ring of Coupled Population Oscillators

et al. 2021

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We show that interactions of inherently chaotic oscillators can lead to coexistence of regular oscillatory regimes and chaotic oscillations in the rings of coupled oscillators provided that the level of interaction between the oscillators exceeds a threshold value. The transformation of the initially chaotic dynamics into the regular dynamics in a number of the coupled oscillators is shown to result from suppression of chaos by separation of certain oscillation periods from the continuous spectra, which are characteristic of chaotic oscillations.

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Section: Discussionmentioning

confidence: 99%

Emergence of Self-Organized Dynamical Domains in a Ring of Coupled Population Oscillators

et al. 2021

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“…For example, as an ecological model [6,7] an encryption machine [8][9][10][11], and a noise generator [12,13], to name a few. Furthermore, in order to explain the emergence of collective phenomena from a tractable framework, coupled logistic maps have been studied numerically [14][15][16] to explain chaotic synchronisation [17][18][19][20] or model effects of diversity and heterogeneity in competing populations [21], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Observation of bifurcations and hysteresis in experimentally coupled logistic maps

Gutiérrez¹,

Cabeza²,

Rubido³

2020

Preprint

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Initially, the logistic map became popular as a simplified model for population growth. In spite of its apparent simplicity, as the population growth-rate is increased the map exhibits a broad range of dynamics, which include bifurcation cascades going from periodic to chaotic solutions. Studying coupled maps allows to identify other qualitative changes in the collective dynamics, such as pattern formations or hysteresis. Particularly, hysteresis is the appearance of different attracting sets, a set when the control parameter is increased and another set when it is decreased -a multi-stable region. In this work, we present an experimental study on the bifurcations and hysteresis of nearly identical, coupled, logistic maps. Our logistic maps are an electronic system that has a discretetime evolution with a high signal-to-noise ratio (∼ 10 6 ), resulting in simple, precise, and reliable experimental manipulations, which include the design of a modifiable diffusive coupling configuration circuit. We find that the characterisations of the isolated and coupled logistic-maps' dynamics agrees excellently with the theoretical and numerical predictions (such as the critical bifurcation points and Feigenbaum's bifurcation velocity). Here, we report multi-stable regions appearing robustly across configurations, even though our configurations had parameter mismatch (which we measure directly from the components of the circuit and also infer from the resultant dynamics for each map) and were unavoidably affected by electronic noise.

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Effects of Patch Number and Dispersal Patterns on Population Dynamics and Synchrony

Ylikarjula

Alaja

Laakso

et al. 2000

Journal of Theoretical Biology

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Models of coupled population oscillators using 1-D maps

Cited by 9 publications

References 24 publications

Emergence of Self-Organized Dynamical Domains in a Ring of Coupled Population Oscillators

Emergence of Self-Organized Dynamical Domains in a Ring of Coupled Population Oscillators

Observation of bifurcations and hysteresis in experimentally coupled logistic maps

Effects of Patch Number and Dispersal Patterns on Population Dynamics and Synchrony

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