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In this paper, we apply a Lyapunov functional approach to Lotka-Volterra systems with infinite delays and feedback controls and establish that the feedback controls have no influence on the attractivity properties of a saturated…
Many recent works on stabilization of nonlinear systems target the case of locally stabilizing an unstable steady state solutions against small perturbation. In this work we explicitly address the goal of driving a system into a…
In this paper, we investigate an initial-boundary-value problem of a reaction-diffusion equation in a bounded domain with a Robin boundary condition and introduce some particular parameters to consider the non-zero flux on the boundary.…
A simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary…
In recent years, classical epidemic models, which assume stationary behavior of individuals, have been extended to include an adaptive heterogeneous response of the population to the current state of the epidemic. However, it is widely…
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…
Main goal: The aim of this note is to propose a modeling approach for assessing the effectiveness of pest biocontrol by natural enemies in diversified agricultural landscapes including several pesticide-based management strategies. Our…
In this paper, we address the problem of globally stabilizing a linear time-invariant (LTI) system by means of a static feedback law whose amplitude and successive time derivatives, up to a prescribed order $p$, are bounded by arbitrary…
This paper presents a framework to perform bifurcation analysis in laboratory experiments or simulations. We employ control-based continuation to study the dynamics of a macroscopic variable of a microscopically defined model, exploring the…
This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…
We consider a multi-population epidemic model with one or more (almost) isolated communities and one mobile community. Each of the isolated communities has contact within itself and, in addition, contact with the outside world but only…
Stabilizing the dynamics of complex, non-linear systems is a major concern across several scientific disciplines including ecology and conservation biology. Unfortunately, most methods proposed to reduce the fluctuations in chaotic systems…
The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…
In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the…
This paper addresses the mean-square optimal control problem for \a class of discrete-time linear systems with a quasi-colored control-dependent multiplicative noise via output feedback. The noise under study is novel and shown to have…
In this paper, we characterize the set of static-state feedbacks that stabilize a given continuous linear-time invariant system pair using dissipative Hamiltonian matrices. This characterization results in a parametrization of feedbacks in…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
We propose a framework to study tipping points in reaction-diffusion equations (RDEs) in one spatial dimension, where the reaction term decays in space (asymptotically homogeneous) and varies linearly with time (nonautonomous) due to an…