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In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by…

Statistical Mechanics · Physics 2018-09-26 Giulio Biroli , Guy Bunin , Chiara Cammarota

The paper focuses on positive solutions to a coupled system of parabolic equations with nonlocal initial conditions. Such equations arise as steady-state equations in an age-structured predator-prey model with diffusion. By using global…

Analysis of PDEs · Mathematics 2010-03-25 Christoph Walker

This paper is concerned with the output feedback stabilization of a reaction-diffusion equation by means of bounded control inputs in the presence of saturations. Using a finite-dimensional controller composed of an observer coupled with a…

Optimization and Control · Mathematics 2022-02-02 Hugo Lhachemi , Christophe Prieur

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

Dynamical Systems · Mathematics 2016-04-20 Marat Akhmet , Aysegul Kivilcim

We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…

Analysis of PDEs · Mathematics 2021-05-10 Wonhyung Choi , Thomas Giletti , Jong-Shenq Guo

For a discrete time Markov chain and in line with Strotz' consistent planning we develop a framework for problems of optimal stopping that are time-inconsistent due to the consideration of a non-linear function of an expected reward. We…

Optimization and Control · Mathematics 2020-01-23 Sören Christensen , Kristoffer Lindensjö

An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…

Dynamical Systems · Mathematics 2023-05-29 Oskar A. Sultanov

We study the well-posedness, steady states and long time behavior of solutions to Vlasov-Fokker-Planck equation with external confinement potential and nonlinear self-consistent interactions. Our analysis introduces newly characterized…

Analysis of PDEs · Mathematics 2024-08-30 Pierre Gervais , Maxime Herda

This paper discusses the stability of an equilibrium point of an ordinary differential equation (ODE) arising from a feed-forward position control for a musculoskeletal system. The studied system has a link, a joint and two muscles with…

Dynamical Systems · Mathematics 2019-04-30 Takahiro Kosugi , Hitoshi Kino , Masaaki Goto , Yuki Matsutani

In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is…

Optimization and Control · Mathematics 2021-12-01 Andrea Zanelli , Quoc Tran Dinh , Moritz Diehl

This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…

In this paper, we consider the dynamics of a delayed reaction-diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary…

Dynamical Systems · Mathematics 2019-10-23 Zuolin Shen , Junjie Wei

Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…

Dynamical Systems · Mathematics 2022-03-25 Abdelmalik Moujahid , Fernando Vadillo

A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…

Populations and Evolution · Quantitative Biology 2025-09-03 Geoffrey R. Hosack , Maud El-Hachem , Nicholas J. Beeton

We consider a modified Lotka-Volterra model applied to the predator-prey system that can also be applied to other areas, for instance the bank system. We show that the model is well-posed (non-negativity of solutions and conservation law)…

Dynamical Systems · Mathematics 2023-12-13 Jorge Pinto , Sandra Vaz , Delfim F. M. Torres

We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…

Pattern Formation and Solitons · Physics 2026-05-05 Mohamed Swailem , Alastair M. Rucklidge

In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…

Optimization and Control · Mathematics 2007-05-23 Iasson Karafyllis , Pierdomenico Pepe , Zhong-Ping Jiang

Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species.…

Quantitative Methods · Quantitative Biology 2017-09-04 Sarbaz H. A. Khoshnaw

We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…

Classical Analysis and ODEs · Mathematics 2012-11-07 Eugene Polulyakh , Vladimir Sharko , Igor Vlasenko

We study the well-posedness and stability of an impedance passive infinite-dimensional linear system under nonlinear feedback of the form $u(t)=\phi(v(t)-y(t))$, where $\phi$ is a monotone function. Our first main result introduces…

Optimization and Control · Mathematics 2025-06-19 Anthony Hastir , Lassi Paunonen