Emergence of chaotic itinerancy in simple ecological systems

Abstract

Chaotic itinerancy is a universal dynamical concept that describes itinerant motion among many different ordered states through chaotic transition in dynamical systems. Unlike the expectation of the prevalence of chaotic itinerancy in high-dimensional systems, we identify chaotic itinerant behavior from a relatively simple ecological system, which consists only of two coupled consumer-resource pairs. The system exhibits chaotic bursting activity, in which the explosion and the shrinkage of the population alternate indefinitely, while the explosion of one pair co-occurs with the shrinkage of the other pair. We analyze successfully the bursting activity in the framework of chaotic itinerancy, and find that large duration times of bursts tend to cluster in time, allowing the effective burst prognosis. We also investigate the control schemes on the bursting activity, and demonstrate that invoking the competitive rise of the consumer in one pair can even elongate the burst of the other pair rather than shorten it.

Noise Characteristics of Molecular Oscillations in Simple Genetic Oscillatory Systems

“…Areas of future research to this end would include, e.g., investigating the role of various regulatory mechanisms besides simple transcription-factor binding for noise con-trol, especially for the oscillation amplitude [26], and the effect of a molecular network on the stochastic dynamics [15,17,30,31]. Further insights into the stochastic dynamics of the biological oscillatory system could be gained by studies of more complex synthetic or natural circuits [12,13] and of the theory of competition-based ecological systems [32,33].…”

Noise characteristics of molecular oscillations in simple genetic oscillatory systems

“…Areas of future research to this end would include, e.g., investigating the role of various regulatory mechanisms besides simple transcription-factor binding for noise control, especially for the oscillation amplitude [26], and the effect of a molecular network on the stochastic dynamics [15,17,30,31]. Further insights into the stochastic dynamics of the biological oscillatory system could be gained by studies of more complex synthetic or natural circuits [12,13] and of the theory of competition-based ecological systems [32,33].…”