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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Winnerless competition in coupled Lotka-Volterra maps.

L A González-Díaz¹, E D Gutiérrez, P Varona

¹Laboratorio de Dinámica Estocástica, Centro de Física, Instituto Venezolano de Investigaciones Científicas, Caracas 1020-A, Venezuela. lagonzalezd@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 16, 2013

Summary

Winnerless competition dynamics in Lotka-Volterra type coupled maps are fully exhibited under specific parameter conditions. These conditions reveal structurally stable heteroclinic cycles, with analytical expressions for residence times derived for N-dimensional cases.

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Area of Science:

Dynamical Systems
Theoretical Ecology
Mathematical Biology

Background:

Winnerless competition describes ecological scenarios where no single species consistently dominates.
Lotka-Volterra models are fundamental in population dynamics.
Coupled map lattices offer a framework for studying complex spatio-temporal dynamics.

Purpose of the Study:

To analyze winnerless competition in discrete-time Lotka-Volterra type coupled maps of arbitrary dimensions.
To deduce conditions for the emergence of structurally stable heteroclinic cycles.
To derive an analytical expression for residence times in N-dimensional systems.

Main Methods:

Analysis of coupled maps with discrete temporal evolution.
Deduction of necessary and sufficient conditions for heteroclinic cycles.
Computational recreation of dynamics for low, intermediate, and high dimensions.
Derivation of an analytical expression for residence times.

Main Results:

Identified necessary and sufficient conditions for structurally stable heteroclinic cycles.
Demonstrated that these conditions fully exhibit winnerless competition dynamics.
Successfully recreated dynamics across various dimensions (low, intermediate, high).
Derived an analytical expression for residence times validated by simulations.

Conclusions:

Winnerless competition in these systems is governed by specific parameter-dependent conditions leading to heteroclinic cycles.
The derived analytical expression for residence times is accurate for N-dimensional systems.
The study provides a comprehensive understanding of winnerless competition dynamics in a generalized Lotka-Volterra framework.