Many mathematical concepts from different branches of mathematics are united to study some properties of cellular automata (CA). Periodicity and chaos (in the sense of sensitive dependence on initial conditions) are studied for 1-dimensional CA. The method of the characteristic polynomial of the...

A fractional order model for nonlocal epidemics is given. Stability of fractional order equations is studied. The results are expected to be relevant to foot-and-mouth disease, SARS and avian flu.

Recent studies in ecology and epidemiology indicate that it is important to include spatial heterogeneity, synchronization and seasonality in the theoretical models. In this work, spatial heterogeneity is introduced via coupled map lattices (CML) and partial differential equations. Stability and...

A model for the evolution of economic systems is defined on a one-dimensional lattice using Pareto optimality. Pareto optimality is shown to maximize the total payoff of all agents in comparison to the Nash optimality. The small-world networks are found to be closer to the real social systems...

Small-world networks (SWN) are found to be closer to the real social systems than both regular and random lattices. Then, a model for the evolution of economic systems is generalized to SWN. The Sznajd model for the two-state opinion formation problem is applied to SWN. Then a simple definition...

Cellular automata model corresponding to Cattaneo's diffusion is constructed. Its phase space is given. Delay is shown to decrease the chaotic (Damage spread) region. Then cellular automata are used to study a stochastic minority game. Payoff memory approach introduced by Smale is used. A...