Related papers: Slow-fast dynamics in a planar parasite--host mode…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
Transitions to absorbing states are of fundamental importance in non-equilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three…
We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…
We study by the strong disorder renormalization group (RG) method the low-energy properties of the one-dimensional Hubbard model with random-hopping matrix-elements $t_{min}<t<t_{max}$, and with random on-site Coulomb repulsion terms $0 \le…
We study the dynamics of a classical disordered macroscopic model completely isolated from the environment reproducing, in a classical setting, the "quantum quench" protocol. We show that, depending on the pre and post quench parameters the…
We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely…
A host-parasite model is considered for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a B-cell always splits into two cells of the same type, the two daughter cells of an A-cell can be…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
The present paper is devoted to the investigation of the long term behavior of a class of singular multi-dimensional diffusion processes that get absorbed in finite time with probability one. Our focus is on the analysis of quasi-stationary…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds for the generalized surface quasi-geostrophic (gSQG) equation.…
This paper investigates the dynamics of a reaction-diffusion system with two free boundaries, modeling the invasion of two cooperative species, where the free boundaries represent expanding fronts. We first analyze the long-term behavior of…
Pattern formation analysis of eco-epidemiological models with cannibalism and disease has been less explored in the literature. Therefore, motivated by this, we have proposed a diffusive eco-epidemiological model and performed pattern…
We present a numerical study of a reaction-diffusion model on a small-world network. We characterize the model's average activity $F_T$ after $T$ time steps and the transition from a collective (global) extinct state to an active state in…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
Mathematical models of infectious disease transmission typically neglect within-host dynamics. Yet within-host dynamics - including pathogen replication, host immune responses, and interactions with microbiota - are crucial not only for…
Bacteria evolve in volatile environments and complex spatial structures. Migration, fluctuations and environmental variability therefore have a significant impact on the evolution of microbial populations. Here, we consider a class of…
Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
Methods of dynamical systems have been used to study homogeneous and isotropic cosmological models with a varying speed of light (VSL). We propose two methods of reduction of dynamics to the form of planar Hamiltonian dynamical systems for…