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This paper studies a two microbial species model in competition for a single resource in the chemostat including general interspecific density-dependent growth rates with distinct removal rates for each species. We give the necessary and…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…
We consider the Hartree and Schr\"{o}dinger equations describing the time evolution of wave functions of infinitely many interacting fermions in three-dimensional space. These equations can be formulated using density operators, and they…
For the stationary nonlinear Schr\"odinger equation $-\Delta u+ V(x)u- f(u) = \lambda u$ with periodic potential $V$ we study the existence and stability properties of multibump solutions with prescribed $L^2$-norm. To this end we introduce…
Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…
In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…
Multistability, the coexistence of multiple stable states, is a cornerstone of nonlinear dynamical systems, governing their equilibrium, tunability, and emergent complexity. Recently, the concept of hidden multistability, where certain…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…
We consider static configurations of bulk scalar fields in extra dimensional models in which the fifth dimension is an $S^1/Z_2$ orbifold. There may exist a finite number of such configurations, with total number depending on the size of…
We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the…
Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression. Because biochemical reactions occur at…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…
We investigate the stability conditions for remote state estimation of multiple linear time-invariant (LTI) systems over multiple wireless time-varying communication channels. We answer the following open problem: what is the fundamental…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
In this paper, from the structural perspective, we propose a new stability analysis approach for the consensus of linear multi-agent systems. Different from the general tools: the Laplacian matrix based method and the Lyapunov's method,…