Age-dependent diffusive Lotka–Volterra type systems

Age-dependent diffusive Lotka-Volterra type systems

In this paper it is shown that the sub-supersolution method works for age-dependent diffusive nonlinear systems with non-local initial conditions. As application, we prove the existence and uniqueness of positive solution for a kind of Lotka-Volterra systems, as well as the blow-up in finite time in a particular case.

Cellular automaton models of driven diffusive Frenkel-Kontorova-type systems.

Three cellular automaton models of increasing complexity are introduced to model driven diffusive systems related to the generalized Frenkel-Kontorova (FK) models recently proposed by Braun et al. [Phys. Rev. E 58, 1311 (1998)]. The models are defined in terms of parallel updating rules. Simulation results are presented for these models. The features are qualitatively similar to those models de...

Diffusive Influence Systems

Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while Turing-complete, influence dynamics of the diffusive type is almost surely asymptotically periodic. Besides resolving the dynamics of a popular family of multiagent systems, t...

Diffusive instabilities in heterogeneous systems

We investigate the behavior of a system composed of two small identical water droplets loaded with an activator-inhibitor system possessing only a single stable steady state and coupled through a third, ‘‘signaling’’ species able to diffuse through the interdroplet medium. Depending on whether the third species is coupled to the activator or the inhibitor, the system can exhibit wave instabilit...

Proof-Assistants Using Dependent Type Systems