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Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…
In this work we focus on a natural class of population protocols whose dynamics are modelled by the discrete version of Lotka-Volterra equations. In such protocols, when an agent $a$ of type (species) $i$ interacts with an agent $b$ of type…
The Duffing oscillator is a paradigm of bistable oscillatory motion in physics, engineering, and biology. Time series of such oscillations are often observed experimentally in a nonlinear system excited by a spontaneously fluctuating force.…
Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…
Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. This notion is new and…
The initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a Volterra integral operator in time of…
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…
We consider an operator-differential expression of the form $$ \ell y=\frac{d^m}{dx^m}\Big(By^{(n)}+Cy\Big), \quad 0<x<1, $$ where $B$ is a linear bounded invertible operator, while $C$ is some finite-dimensional linear operator relatively…
We consider an ecological system governed by Lotka-Volterra dynamics and an example of an economic system as a mesomarket with perfect competition. We propose a mechanism for cooperative self-regulation that enables the system under…
The increase in system complexity paired with a growing availability of operational data has motivated a change in the traditional control design paradigm. Instead of modeling the system by first principles and then proceeding with a…
We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are…
The Douglas-Rachford algorithm can be represented as the fixed point iteration of a firmly nonexpansive operator. When the operator has no fixed points, the algorithm's iterates diverge, but the difference between consecutive iterates…
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in…
A nonlinearly coupled system of bouncing balls is shown to exhibit features like self-organised-criticality (SOC) and punctuated equilibrium (PE) in suitable parameter domains. The temporal evolution of the non-stationary amplitudes is…
Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…
We consider a bilinear control problem for the wave equation on a torus of arbitrary dimension. We show that the system is globally approximately controllable in arbitrarily small times from a dense family of initial states. The control…
Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…