New insights in stability analysis of delayed Lotka–Volterra systems

Abstract

Most of the reported Lotka–Volterra examples have at most one stability interval for the delay parameters. Furthermore, the existing methods fall short in treating more general case studies. Inspired by some recent results for analyzing the stability of time-delay systems, this paper focuses on a deeper characterization of the stability of Lotka–Volterra systems w.r.t. the delay parameters. More precisely, we will introduce the recently-proposed frequency-sweeping approach to study the complete stability problem for a broad class of linearized Lotka–Volterra systems. As a result, the whole stability delay-set can be analytically determined. Moreover, as a significant byproduct of the proposed approach, some Lotka–Volterra examples are found to have multiple stability delay-intervals. To the best of the authors’ knowledge, such a characterization represents a novelty for having some insights in the population dynamics: in some situations, a longer maturation period of species is helpful for the stability of a population system.