Related papers: Oscillatory Dynamics in Rock-Paper-Scissors Games …
Building upon the eco-evolutionary game dynamics framework established by Tilman et al., we investigate stochastic fluctuations in a two-strategy system incorporating environmental feedback mechanisms, where the payoff matrix exhibits…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
We study the emergent dynamics resulting from the infinite volume limit of the mean-field dissipative dynamics of quantum spin chains with clustering, but not time-invariant states. We focus upon three algebras of spin operators: the…
We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
In this paper, we investigate the stability of the configurations of harmonic oscillator potential that are directly proportional to the square of the displacement. We derive expressions for fluctuations in partition function due to…
One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described…
Activated escape of a Brownian particle from the domain of attraction of a stable focus over a limit cycle exhibits non-Kramers behavior: it is non-Poissonian. When the attractor is moved closer to the boundary oscillations can be discerned…
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from…
Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly…
In a static environment, optional participation and a local agglomeration of cooperators are found to be beneficial for the occurrence and maintenance of cooperation. In the optional public goods game, the rock-scissors-paper cycles of…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
Large entropy fluctuations in an equilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2--freedom strongly chaotic Hamiltonian model described by the modified Arnold cat map. The rise…
Suppose a two-dimensional dynamical system has a stable attractor that is surrounded by an unstable limit cycle. If the system is additively perturbed by white noise, the rate of escape through the limit cycle will fall off exponentially as…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
This work deals with the influence of the neighborhood in simple rock-paper-scissors models of biodiversity. We consider the case of three distinct species which evolve under the standard rules of mobility, reproduction and competition. The…
We investigate a six-species class of May-Leonard models leading to formation two types of competing spatial domains, each one inhabited by three-species with their own internal cyclic rock-paper-scissors dynamics. We study the resulting…