Related papers: Characterizing long transients in consumer-resourc…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
Drawing on the understanding of the logistic map, we propose a simple predator-prey model where predators and prey adapt to each other, leading to the co-evolution of the system. The special dynamics observed in periodic windows contribute…
In the present article, we demonstrate the emergence and existence of the spiral wave chimera-like transient pattern in coupled ecological systems, composed of prey-predator patches, where the patches are connected in a three-dimensional…
In this work we study the process of mutant invasion on an example of a consumer-resource system with annual character of the behavior. Namely, individuals are active during seasons of fixed length separated by winter periods. All…
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…
In this paper, we develop a method of analyzing long transient dynamics in a class of predator-prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the…
This note is a brief review of the analysis of long transients in dynamical systems. The problem of long transients arose in many disciplines, from physical and chemical kinetic to biology and even social sciences. Detailed analysis of…
Spatio-temporal complexity of ecological dynamics has been a major focus of research for a few decades. Pattern formation, chaos, regime shifts and long transients are frequently observed in field data but specific factors and mechanisms…
Mathematical modeling and analysis of spatial-temporal population distributions of interacting species have gained significant attention in biology and ecology in recent times. In this work, we investigate a Bazykin-type prey-predator model…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
We study a discrete-time interacting particle system with continuous state space which is motivated by a mathematical model for turnover through branching in actin filament networks. It gives rise to transient clusters reminiscent of actin…
Dormancy is a widespread adaptive strategy that enables populations to persist in fluctuating environments, yet how its benefits depend on the temporal structure of environmental variability remains unclear. We examine how dormancy…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in…
We study the long time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural networks model. The system has a finite number of possible states so it is not possible to use…
In this paper we study the long term evolution of a continuous time Markov chain formed by two interacting birth-and-death processes. The interaction between the processes is modelled by transition rates which are functions with suitable…
We study the spatio-temporal dynamics of the generalized repressilator, a system of coupled repressing genes arranged in a directed ring topology, and give analytical conditions for the emergence of a cascade of unstable periodic orbits…