Related papers: Asymptotic behavior of spatially distributed repli…
In equilibrium systems with short-ranged interactions, the relative stability of different thermodynamic states generally does not depend on system size (as long as this size is larger than the interaction range). Here, we use a large…
We consider the class of SIS epidemic models in which a large population of individuals chooses whether to adopt protection or to remain unprotected as the epidemic evolves. For a susceptible individual, adopting protection reduces the…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…
We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is…
We study small random perturbations by additive white-noise of a spatial discretization of a reaction-diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
We address a distributed adaptive control methodology for nonlinear interconnected systems possibly affected by network anomalies. In the framework of adaptive approximation, the distributed controller and parameter estimator are designed…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
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…
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…
A replicator equation with explicit space and global regulation is considered. This model provides a natural framework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the…
We establish the local input-to-state stability of a large class of disturbed nonlinear reaction-diffusion equations w.r.t. the global attractor of the respective undisturbed system.
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
Swarm stability is concerned for descriptor compartmental networks with linear time-invariant protocol. Compartmental network is a specific type of dynamical multi-agent system. Necessary and sufficient conditions for both consensus and…