Related papers: Equilibria for an aggregation model with two speci…
We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are…
In this paper we find and classify all patterns for a single locus three- and four-allele population genetics models in continuous time. A pattern for a $k$-allele model means all coexisting locally stable equilibria with respect to the…
The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on…
Transport models of growth hormones can be used to reproduce the hormone accumulations that occur in plant organs. Mostly, these accumulation patterns are calculated using time step methods, even though only the resulting steady state…
We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…
Swarms of large numbers of agents appear in many biological and engineering fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been observed in many models of large population swarms. However, many reduced models for…
We constructed a model that evolved from a non-equilibrium state to an equilibrium state. The model only needs two basic coefficients, including self-similar coefficients and non-equilibrium coefficients. The coefficients of the model can…
Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct…
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…
In this paper, we study a nonlocal evolution system. We apply abstract results from the bifurcation theory to obtain the existence of coexistence states. Their stability are investigated as well.
Insects and birds are often faced by opposing requirements for agile and stable flight. Here, we explore the interplay between aerodynamic effort, maneuverability, and stability in a model system that consists of a $\Lambda$-shaped flyer…
Random non-reciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system towards pattern formation. The enhanced stability is an exact result when the number of species approaches…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the…
The conditions of multi-phase equilibrium are solved for generic polydisperse systems. The case of multiple polydispersity is treated, where several properties (e.g. size, charge, shape) simultaneously vary from one particle to another. By…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…