Emergence of extreme events in networks of parametrically coupled chaotic populations

Abstract

We consider a collection of populations modelled by the prototypical chaotic Ricker map, relevant to the population growth of species with non-overlapping generations. The growth parameter of each population patch is influenced by the local mean field of its neighbourhood, and we explore the emergent patterns in such a parametrically coupled network. In particular, we examine the dynamics and distribution of the local populations, as well as the total biomass. Our significant finding is the following: When the range of coupling is sufficiently large, namely, when enough neighbouring populations influence the growth rate of a population, the system yields remarkably large biomass values that are very far from the mean. These extreme events are relatively rare and uncorrelated in time. We also find that at any point in time, exceedingly large population densities emerge in a few patches, analogous to an extreme event in space. Thus, we suggest a new mechanism in coupled chaotic systems that naturally yield extreme events in both time and space.

Biased random walkers and extreme events on the edges of complex networks

“…Over the years, this proposition was observed in many different settings. For instance, this feature been theoretically reported in a network of coupled chaotic maps [10], in stochastic processes such as Brownian motion in an external potential [11], and in biased random walks on networks [12]. However, it appears that in the case of interactions among agents, the extreme events created by the agents can possibly have a different profile for the probability for the occurrence of extreme events [13,14].…”

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

“…Recent theoretical progress has tended to concentrate on particular aspects of coupling functions, with some being more focused on the overall interactions or qualitative states, while others study unique characteristics of coupling functions and how they affect the overall interactions [10][11][12][13][14][15][16]. In this way, the coupling functions play important roles in the phenomena and the qualitative states resulting from the interactions.…”

“…Examples include synchronization [9,[17][18][19], amplitude and oscillation death [20][21][22][23] and the low-dimensional dynamics of ensembles [24][25][26]. Much attention has also been devoted to coupling functions and networks [10,12,13,27,28]. Coupling functions can also have important implications if used in a nontraditional way like, for example, ones that are of biharmonic form or non-pairwise coupling functions [10,11,29,30].…”

Enhancement of extreme events through the Allee effect and its mitigation through noise in a three species system

“…Broadly speaking, the statistical features of deterministic systems is an active research direction that can lead to understanding extreme events that arise in the context of deterministic dynamics 12 , 13 . The search for dynamical systems that yield extreme events, without the drive of external stochastic influences or intrinsic random fluctuations, is a focus of much ongoing research effort from the point of view of basic understanding of complex systems 14 – 17 . Additionally, such probabilistic outcomes in dynamical systems are most relevant in the applied context as well, such as in engineering sciences where this direction of research leads to better assessment of risks 18 .…”