Related papers: Asymptotic dynamics of attractive-repulsive swarms
We use traveling-wave theory to derive expressions for the rate of accumulation of deleterious mutations under Muller's ratchet and the speed of adaptation under positive selection in asexual populations. Traveling-wave theory is a…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
We consider swarms formed by populations of self-propelled particles with attractive long-range interactions. These swarms represent multistable dynamical systems and can be found either in coherent traveling states or in an incoherent…
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…
We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering towards a weighted average heading. We consider the class of so-called $p$-alignment hydrodynamics, based on $2p$-Laplacians, and weighted by a general…
Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…
In this paper, we mainly investigate the spreading dynamics of a nonlocal diffusion KPP model with free boundaries which is firstly explored in time almost periodic media. As the spreading occurs, the long-run dynamics are obtained.…
We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their…
We study the real time evolution of the correlation functions in a globally quenched interacting one dimensional lattice system by means of time adaptive density matrix renormalization group. We find a clear light-cone behavior quenching…
The availability of new data sources on human mobility is opening new avenues for investigating the interplay of social networks, human mobility and dynamical processes such as epidemic spreading. Here we analyze data on the time-resolved…
We study a PDE model for dynamics of susceptible-infected interactions. The dispersal of susceptibles is via diffusion and repellent taxis as they move away from the increasing density of infected. The diffusion of infected is a nonlinear,…
We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the…
The spread of disease through a physical-contact network and the spread of information about the disease on a communication network are two intimately related dynamical processes. We investigate the asymmetrical interplay between the two…
Swarming phenomena are ubiquitous in various physical, biological, and social systems, where simple local interactions between individual units lead to complex global patterns. A common feature of diverse swarming phenomena is that the…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: short-range kernels which restrict the communication to local geometric balls, and anisotropic…