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The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…
The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown…
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…
In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many…
Recurrent neural policies are widely used in partially observable control and meta-RL tasks. Their abilities to maintain internal memory and adapt quickly to unseen scenarios have offered them unparalleled performance when compared to…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
We present a simple two-dimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations. The power law…
The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modelling of crowd dynamics, which also leads to…
The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
We investigate cyclic dominance models and their extensions to both network systems and reaction-diffusion frameworks. Using linear stability analysis, we establish the relationship between the stability of synchronized states in network…