Adaptation and its impact on the dynamics of a system of three competing populations

We investigate how the adaptation of the competition coefficients of the competing populations for the same limited resource influences the system dynamics in the regions of the parameter space, where chaotic motion of Shilnikov kind exists. We present results for two characteristic values of the competition coefficient adaptation factor α*. The first value α*=−0.05 belongs to the small interval of possible negative values of α*. For this, α* a transition to chaos by period-doubling bifurcations occurs and a window of periodic motion exists between the two regions of chaotic motion. With increasing α*, the system becomes more dissipative and the number of the windows of periodic motion increases. When α*=1.0, a region of transient chaos is observed after the last window of periodic motion. We verify the picture of the system dynamics by power spectra, histograms and autocorrelations and calculate the Lyapunov exponents and Kaplan–Yorke dimension. Finally we discuss the eligibility of the investigated system for a topological analysis