Related papers: Stationary Stability for Evolutionary Dynamics in …
This paper study the hyperexponential stabilization for infinite-dimensional system on Hilbert space by a distributed time depending control law. The well-posedness of the closed loop for every time is obtained through the use of maximal…
We introduce a notion of "local stability in permutations" for finitely generated groups. If a group is sofic and locally stable in our sense, then it is also locally embeddable into finite groups (LEF). Our notion is weaker than the…
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…
The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…
One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats…
The stability criteria of rapid mass transfer and common-envelope evolution are fundamental in binary star evolution. They determine the mass, mass ratio, and orbital distribution of many important systems, such as X-ray binaries, type Ia…
The concept of input-to-state stability (ISS) proposed in the late 1980s is one of the central notions in robust nonlinear control. ISS has become indispensable for various branches of nonlinear systems theory, such as robust stabilization…
We study integral-to-integral input-to-state stability for infinite-dimensional linear systems with inputs and trajectories in $L^p$-spaces. We start by developing the corresponding admissibility theory for linear systems with unbounded…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
In this paper nonstandard finite difference (NSFD) schemes of two metapopulation models are constructed. The stability properties of the discrete models are investigated by the use of a generalization of Lyapunov stability theorem. Due to…
The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under…
Several groups have recently modeled evolutionary transitions from an ancestral allele to a beneficial allele separated by one or more intervening mutants. The beneficial allele can become fixed if a succession of intermediate mutants are…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only…
In this paper we propose a Moran model that describes the population dynamics of two types: While the first type has a selective advantage during reproduction, the second type can avoid replacement during reproduction with some positive…
We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from…
Input-to-state stability (ISS) allows estimating the impact of inputs and initial conditions on both the intermediate values and the asymptotic bound on the solutions. ISS has unified the input-output and Lyapunov stability theories and is…
To investigate the origin of cooperative behaviors, we developed an evolutionary model of sequential strategies and tested our model with computer simulations. The sequential strategies represented by stochastic machines were evaluated…
We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…
We consider stability in a class of random non-linear dynamical systems characterised by a relaxation rate together with a Gaussian random vector field which is white-in-time and spatial homogeneous and isotropic. We will show that in the…