Related papers: Globally synchronized oscillations in complex cycl…
We analyze the Hunter vs Rabbit game on graph, which is a kind of model of communication in an adhoc mobile network. Let $G$ be a cycle graph with $N$ nodes. The hunter can move from a vertex to another vertex on the graph along an edge.…
In this work we focus on a natural class of population protocols whose dynamics are modelled by the discrete version of Lotka-Volterra equations. In such protocols, when an agent $a$ of type (species) $i$ interacts with an agent $b$ of type…
Natural birth and death are fundamental mechanisms of population dynamics in ecosystems and have played pivotal roles in shaping population dynamics. Nevertheless, in studies of cyclic competition systems governed by the rock-paper-scissors…
We study a three-species cyclic model whose organisms are vulnerable to contamination with an infectious disease which propagates person-to-person. We consider that individuals of one species perform an evolutionary self-preservation…
A metapopulation structure in landscape ecology comprises a group of interacting spatially separated subpopulations or patches of the same species that may experience several local extinctions. This makes the investigation of survivability…
This work reports on two related investigations of stochastic simulations which are widely used to study biodiversity and other related issues. We first deal with the behavior of the Hamming distance under the increase of the number of…
The Rock-Paper-Scissors (RPS) game is a classic non-cooperative game widely studied in terms of its theoretical analysis as well as in its applications, ranging from sociology and biology to economics. Many experimental results of the RPS…
Antipredator behaviour is a self-preservation strategy present in many biological systems, where individuals join the effort in a collective reaction to avoid being caught by an approaching predator. We study a nonhierarchical tritrophic…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
Cyclic, nonhierarchical interactions among biological species represent a general mechanism by which ecosystems are able to maintain high levels of biodiversity. However, species coexistence is often possible only in spatially extended…
We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged analogue of the Lorenz attractor. The attractors emerge near the…
Numerous elements drive the spread of infectious diseases in complex real-world networks. Of particular interest is social behaviors that evolve in tandem with the spread of disease. Moreover, recent studies highlight the importance of…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the…
The importance of pulse-coupled oscillators (PCOs) in biology and engineering has motivated research to understand basic properties of PCO networks. Despite the large body of work addressing PCOs, a global synchronization result for…
Synchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all…
The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…
Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics…
Quantifying population dynamics is a fundamental challenge in ecology and evolutionary biology, particularly for species that are cryptic, microscopic, or extinct. Traditional approaches rely on continuous representations of population…
We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a…