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We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal…
The collective swimming of soft robots in an infinite viscous fluid is an emergent phenomenon due to the non-reciprocal hydrodynamic interactions between individual swimmers. These physical interactions give rise to unique spatiotemporal…
The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model…
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…
In recent years, there has been considerable interest in understanding the motion in Hamiltonian systems when phase space is divided into stochastic and integrable regions. This paper studies one aspect of this problem, namely, the motion…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…
In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…
In this paper, an attempt is made to understand the dynamics of a three-dimensional discrete fractional-order eco-epidemiological model with Holling type II functional response. We first discretize a fractional-order predator-prey-parasite…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
The spatiotemporal structure of reactive media supporting a solitary spiral wave is studied for systems where the local reaction law exhibits a period-doubling cascade to chaos. This structure is considerably more complex than that of…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
We show that a two-dimensional system of flocking microswimmers interacting hydrodynamically can be expressed using a Hamiltonian formalism. The Hamiltonian depends strictly on the angles between the particles and their swimming…
Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these…
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…
We study the spatial distributions of two randomly interacting species, in the presence of an external multiplicative colored noise. The dynamics of the ecosystem is described by a coupled map lattice model. We find a nonmonotonic behavior…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…