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- Title
SUPPRESSESG CHAOS IN POPULATION DYNAMICS DISCRETE MODELS BY ADDING PERIODIC PULSES TO THE SYSTEM VARIABLES.
- Authors
Dumitru, Deleanu
- Abstract
The inability to predict the evolution of population dynamics in the presence of chaos can lead to catastrophic situations so chaos-control techniques must be applied to direct the system towards a predictable behaviour. This can be done either by controlling chaos, so the system's final state is an unstable periodic orbit embedded in the strange attractor of the original system, or by suppressing chaos and producing a controlled regular state of an auxiliary system. A simple and efficient algorithm that suppress chaos by adding constant and periodic pulses to the dynamic system variables has been proposed by Guemez and Mathias. The pulses are introduced into the system either in multiplicative or additive ways The performance of the method depends critically on the period and the strength of the feedback. With [he aim of proving the merits of the method and providing multiple numerical evidences concerning the ability of the approach to change the chaotic state into a periodic one, in the paper we analysed a discrete-time two species food chain model having a rich Spectrum of dynamical behaviours including chaos. Because the System parameters were chosen so the system behaves chaotic but close enough to a period-6 window in the bifurcation diagram, we concentrated mainly in stabilizing orbits having periods multiple of six. However, other cases were also considered. The influence of feedback strengths on the stabilization process was highlighted by computing and drawing colour maps presenting the period of the stabilized orbits. They show-that even small interventions on system variables can direct the system to the desired goal.
- Subjects
POPULATION dynamics; LOTKA-Volterra equations; PREDATION; ECOLOGICAL food chain models; CHAOS theory
- Publication
Journal of Marine Technology & Environment, 2018, Issue 1, p15
- ISSN
1844-6116
- Publication type
Article