Related papers: Stochastic Extinction, An Average Lyapunov Functio…
We consider ecological difference equations of the form $X_{t+1}^i =X_t^i A_i(X_t)$ where $X_t^i$ is a vector of densities corresponding to the subpopulations of species $i$ (e.g. subpopulations of different ages or living in different…
We analyze a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time (stochastic difference equations), continuous…
In this paper we consider the stability of a class of deterministic and stochastic SEIRS epidemic models with delay. Indeed, we assume that the transmission rate could be stochastic and the presence of a latency period of $r$ consecutive…
A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially…
Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist…
This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate…
A generalized Lyapunov method is outlined which predicts global stability of a broad class of dissipative dynamical systems. The method is applied to the complex Lorenz model and to the Navier-Stokes equations. In both cases one finds…
We study sporadic randomness by means of a non-extensive form of Lyapunov coefficient. We recover from a different perspective the same conclusion as that of an earlier work, namely, that the ordinary Pesin theorem applies (P.Gaspard and…
We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant…
We consider the extinction regime in the spatial stochastic logistic model in $\mathbb{R}^d$ (a.k.a. Bolker--Pacala--Dieckmann--Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space…
A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…
The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and…
We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system…
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…
We consider the unexploited/exploited logistic equation and study the stability of equilibrium points through Lyapunov functions. Then, we apply first and second order optimality conditions for the optimal control of the total biomass…
A family of heterogeneous mean-field systems with jumps is analyzed. These systems are constructed as a Gibbs measure on block graphs. When the total number of particles goes to infinity, a law of large numbers is shown to hold in a…
Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…
Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…