Complexity Measure in Simple Type Food Chain System

Abstract

Study of complexities arising during evolution of a food chain system has been investigated. Regular and chaotic motions have been observed for certain sets of values of a parameter of the system. For some detailed further study, the continuous model of food chain has been transformed into discrete model by using Euler's method. Various measurable quantities for emergence of chaos, like Lyapunov exponents, topological entropies, correlation dimensions, have been numerically calculated and represented through plots. Finally, the chaos indicator, named Dynamic Lyapunov Indicator (DLI), has been used to identify clearly chaotic and regular motion.