相关论文: Analysis of a cross-diffusion model for rival gang…
We present an agent-based model to simulate gang territorial development motivated by graffiti marking on a two-dimensional discrete lattice. For simplicity, we assume that there are two rival gangs present, and they compete for territory.…
We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing a previously-published model to account for $K$ groups instead of two groups. We then analyze this…
For the gang territoriality model \begin{align*} \begin{cases} u_t = D_u \Delta u + \chi_u \nabla \cdot (u \nabla w), \\ v_t = D_v \Delta v + \chi_v \nabla \cdot (v \nabla z), \\ w_t = -w + \frac{v}{1+v}, \\ z_t = -z + \frac{u}{1+u},…
In this work, we introduce a compartmental advection-diffusion network model to describe the propagation of stress in a population situated in two interconnected spatial zones during a disaster situation. The model accounts for interactions…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
We study the well-known sociological phenomenon of gang aggregation and territory formation through an interacting agent system defined on a lattice. We introduce a two-gang Hamiltonian model where agents have red or blue affiliation but…
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing…
We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic behavior is deduced from the gradient flow associated to…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity. We show that the assumption of a populations natural tendency towards crime significantly changes the…
A new non-conservative stochastic reaction-diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport…
Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We…
This paper introduces a reaction-advection-diffusion system that models interactions among three actors: a target, a partaker, and a guardian. The framework is versatile, capturing phenomena ranging from the emergence and movement of crime…
We study the equilibrium points of a system of equations corresponding to a Bass based model that describes the diffusion of two brands in competition. To increase the understanding of the effects of the cross-brand parameters, we perform a…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
We study a kinetically constrained lattice glass model in which continuous local densities are randomly redistributed on neighbouring sites with a kinetic constraint that inhibits the process at high densities, and a random bias accounting…
We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…
A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy,…