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Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
This paper focuses on the problem of constructing time-varying feedback laws that asymptotically stabilize a given part of the state variables for nonlinear control-affine systems. It is assumed that the class of systems under consideration…
Mathematical modeling and analysis of spatial-temporal population distributions of interacting species have gained significant attention in biology and ecology in recent times. In this work, we investigate a Bazykin-type prey-predator model…
We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a…
A conservation law and stability, recovering phenomena and characteristic patterns of a nonlinear dynamical system have been studied and applied to biological and ecological systems. In our previous study, we proposed a system of symmetric…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
In this paper, we study a diffusive Lotka-Volterra competition model under homogeneous Dirichlet boundary conditions. We shall discuss the effects of dispersal rate and spatial heterogeneity on population dynamics. More precisely, we…
We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the…
We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary…
The broad application range of the predator-prey modelling enabled us to apply it to represent the dynamics of the work-employment system. For the adopted period, we conclude that this dynamics is chaotic in the beginning of the time series…
The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…
The notions of taxis and kinesis are introduced and used to describe two types of behavior of an organism in non-uniform conditions: (i) Taxis means the guided movement to more favorable conditions; (ii) Kinesis is the non-directional…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
This paper addresses the problems of stabilization, robust control, and observer design for nonlinear systems. We build upon recently a proposed method based on contraction theory and convex optimization, extending the class of systems to…
In this work, we introduce a compartmental advection-diffusion network model to describe the propagation of stress in a population situated in two interconnected spatial zones during a disaster situation. The model accounts for interactions…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…
In this paper we study the effects of constraints on the dynamics of an adaptive segregation model introduced by Bischi and Merlone (2011). The model is described by a two dimensional piecewise smooth dynamical system in discrete time. It…
We give a characterization of the controllability for discrete-time linear systems with convex output constraints. It extends all previously known characterizations in the literature, as well as our previous results on controllability of…
Using Mickens nonstandard method, we obtain a discrete family of nonautonomous eco-epidemiological models that include general functions corresponding to the predation of the infected and uninfected preys. We obtain results on the…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…