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In bio-social models, cooperative behaviour has evolved as an adaptive strategy, playing multi-functional roles. One of such roles in populations is to increase the success of survival and reproduction of individuals and their families or…
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrodinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior,…
In this paper, we inspect well-known population genetics and social dynamics models. In these models, interacting individuals, while participating in a self-organizing process, give rise to the emergence of complex behaviors and patterns.…
One of the most salient spatio-temporal patterns in population ecology is the synchronization of fluctuating local populations across vast spatial extent. Synchronization of abundance has been widely observed across a range of spatial…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the…
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…
We study analytically and numerically a model metabolic cycle composed of an arbitrary number of species of catalytically active particles. Each species converts a substrate into a product, the latter being used as the substrate by the next…
Non-linear maps can possess various dynamical behaviors varying from stable steady states and cycles to chaotic oscillations. Most models assume that individuals within a given population are identical ignoring the fundamental role of…
Gradual changes in exploitation, nutrient loading, etc. produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of…
Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…
In this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…
Many ecological populations are known to display a cyclic behavior with period 2. Previous work has shown that when a metapopulation (group of coupled populations) with such dynamics is allowed to interact via nearest neighbor dispersal in…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous…
The dynamical rules in auxiliary stochastic process that generates the biased ensemble of rare events are non-local. For the systems with one type of particle, it is shown that there are special cases for which the generators of effective…