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The principle of linearized stability is established for age-structured diffusive populations incorporating nonlinear death and birth processes. More precisely, asymptotic exponential stability is shown for equilibria for which the…
Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive.…
We establish the relation between local stability of equilibria and slopes of critical curves for a specific class of difference equations. We then use this result to give global behavior results for nonnegative solutions of the system of…
The theoretical understanding of pattern formation in active systems remains a central problem of interest. Heterogeneous flocks made up of multiple species can exhibit a remarkable diversity of collective states that cannot be obtained…
We study the nonlinear stability of a large class of inhomogeneous steady state solutions to the Hamiltonian Mean Field (HMF) model. Under a simple criterion, we prove the nonlinear stability of steady states which are decreasing functions…
Reconnection outflows are regions of intense recent scrutiny, from in situ observations and from simulations. These regions are host to a variety of instabilities and intense energy exchanges, often even superior to the main reconnection…
Noise or fluctuations play an important role in the modeling and understanding of the behavior of various complex systems in nature. Fokker-Planck equations are powerful mathematical tool to study behavior of such systems subjected to…
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…
We propose an extension to the ISM of flocking and swarming. The model has been introduced to explain certain dynamic features of swarming (second sound, a lower than expected dynamic critical exponent) while preserving the mechanism for…
We first give a complete linearized stability analysis around stationary solutions of the Mullins-Sekerka flow with $90^\circ$ contact angle in two space dimensions. The stationary solutions include flat interfaces, as well as arcs of…
We study point-like polarizable particles confined in a 1D very elongated trap within the evanescent field of an optical nano-fiber or nano-structure. When illuminated transversely by coherent light, collective light scattering into…
We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the…
This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population…
We consider the Czir\'ok model for collective motion of locusts along a one-dimensional torus. In the model, each agent's velocity locally interacts with other agents' velocities in the system, and there is also exogenous randomness to each…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
Nonlinear solitary solutions to the Vlasov-Poisson set of equations are studied in order to investigate their stability by employing a fully-kinetic simulation approach. The study is carried out in the ion-acoustic regime for a…
Clustering is one of the mayor collective phenomena observed in active matter. We study the overdamped motion of interacting active Brownian particles in two dimensions. An instability in the pair correlation function causes the onset of…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…