Related papers: Spectral control for ecological stability
We report on a significant improvement of the classical time-delayed feedback control method for stabilization of unstable periodic orbits or steady states. In an electronic circuit experiment we were able to realize time-varying and…
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…
A simple method to perform chaos control without the need of complex numerical and analytical calculations is proposed. The method works for dynamical systems with bounded solutions and in the trivial case of constant Jacobians.
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
The concept of evolutionarily stability and its relation with the fixed points of the replicator equation are important aspects of evolutionary game dynamics. In the light of the fact that oscillating state of a population and individuals…
This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a…
Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small…
For a physical or biological model whose dynamics is described by a higher order difference equation $u_{n+1}=f(u_n,u_{n-1}, \dots, u_{n-k+1})$, we propose a version of a target oriented control $u_{n+1}=cT+(1-c)f(u_n,u_{n-1}, \dots,…
Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with…
The Lotka-Volterra system is a set of ordinary differential equations describing growth of interacting ecological species. This model has gained renewed interest in the context of random interaction networks. One of the debated questions is…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems…
Biological systems (among others) may respond to a large variety of distinct external stimuli, or signals. These perturbations will generally be presented to the system not singly, but in various combinations, so that a proper understanding…
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…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
We consider systems of weakly interacting fermions on a lattice. The corresponding free fermionic system is assumed to have a ground state separated by a gap from the rest of the spectrum. We prove that, if both the interaction and the free…
Mutualisms are key for structuring ecological communities, but they are sensitive to environmental change and fluctuations in population size. Consequently, how mutualisms achieve stability remains an open question in ecological theory.…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…