How great an effect does self-generated spatial structure have on logistic population growth? Results are described from an individual based model (IBM) with spatially localised dispersal and competition, and from a deterministic approximation to the IBM describing the dynamics of the first and second spatial moments. The dynamical system incorporates a novel closure that gives a close approxim...

This paper denes and investigates the ergodic proper-ties of the entropy of a countable partition of a fuzzy dynamical sys-tem at different points of the state space. It ultimately introducesthe local fuzzy entropy of a fuzzy dynamical system and proves itto be an isomorphism invariant.

If a galaxy cluster is effectively in dynamical equilibrium then all galaxy populations within the cluster must have distributions in velocity and position that individually reflect the same underlying mass distribution, although the derived virial masses can be quite different. Specifically, within the CNOC cluster sample the virial radius of the red galaxy population is, on the average, a fac...

We obtain sufficient conditions for the stability of the synchronized solution for certain classes of coupled dynamical systems. This is accomplished by finding an analytic expression for the transverse Lyapunov exponent through spectral analysis. We then indicate some applications to population dynamics.

This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal r...

In this paper, we construct a linear differential system in both continuous time and discrete time to model HIV transmission on the population level. The main question is the determination of parameters based on the posterior information obtained from statistical analysis of the HIV population. We call these parameters dynamic constants in the sense that these constants determine the behavior o...

Coarsening underlies numerous natural processes including phase separation, grain growth, soap bubbles, and species segregation. It is generally believed that coarsening systems exhibit dynamical scaling [1], i.e., the typical domain size grows algebraically with time, `(t) ∼ t. The exponent α is usually independent of many details of the system such as the spatial dimension. However, little is...

We discuss the use of the rotation number to detect periodic solutions in a parameterized family of discrete dynamical systems. Furthermore, we give an algorithm to compute the rotation number and apply this algorithm to a sh population model.