Related papers: Estimates for solutions in a predator-prey model d…
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…
Recently, energetic variational approach was employed to derive models for non-isothermal electrokinetics by Liu et. al \cite{Liu-Wu-Liu-CMS2018}. In particular, the Poisson-Nernst-Planck-Fourier (PNPF) system for the dynamics of $N$-ionic…
In this paper, a delay Vlasov-Fokker-Planck equation associated to a stochastic interacting particle system with delay is investigated analytically. Under certain restrictions on the parameters well-posedness and ergodicity of the…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
We study an individual-based predator-prey model of biological coevolution, using linear stability analysis and large-scale kinetic Monte Carlo simulations. The model exhibits approximate 1/f noise in diversity and population-size…
This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a…
This paper extends the deterministic Lyapunov-based stabilization framework to random hyperbolic systems of conservation laws, where uncertainties arise in boundary controls and initial data. Building on the finite volume discretization…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
A general framework for age-structured predator-prey systems is introduced. Individuals are distinguished into two classes, juveniles and adults, and several possible interactions are considered. The initial system of partial differential…
We study singularly perturbed systems that exhibit input-to-state stability (ISS) with fixed-time properties in the presence of bounded disturbances. In these systems, solutions converge to the origin within a time frame independent of…
We consider large but finite systems of identical agents on the line with up to next nearest neighbor asymmetric coupling. Each agent is modelled by a linear second order differential equation, linearly coupled to up to four of its…
In this work, we study a generalized Fisher market model that incorporates social influence. In this extended model, a buyer's utility depends not only on their own resource allocation but also on the allocations received by their…
Gravitational and electrostatic interactions are fundamental examples of systems with long-range interactions. Equilibrium properties of simple models with long-range interactions are well understood and exhibit exotic behaviors : negative…
Dispersal between different habitats influences the dynamics and stability of populations considerably. Furthermore, these effects depend on the local interactions of a population with other species. Here, we perform a general and…
We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the…
We investigate the general asymptotic behaviour of Friedman-Robertson-Walker (FRW) models with an inflaton field, scalar-tensor FRW cosmological models and diagonal Bianchi-IX models by means of Liapunov's method. This method provides…
We consider systems of interacting particles which are described by a second order Langevin equation. The class of equations considered includes the situation where the particle evolution is governed by Hamiltonian dynamics with additional…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
Cooperative dynamics are common in ecology and population dynamics. However, their commonly high degree of complexity with a large number of coupled degrees of freedom renders them difficult to analyse. Here we present a graph-theoretical…
This paper is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. To overcome the analytical obstacle caused by the cross-diffusion…