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.

The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without delay), hawk–dove–retaliate and prisoner's dilemma...

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...

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...

The stability of some spatial asymmetric games is discussed. Both linear and nonlinear asymptotic stability of asymmetric hawk-dove and prisoner's dilemma are studied. Telegraph reaction diffusion equations for the asymmetric spatial games are presented. Asymmetric games of parental investment...

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...

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...

An inhomogeneous version of Ito–Matsuzaki model for earthquakes is introduced. This model obeys Gutenberg–Richter’s law with excellent estimations for both the b-value and the fractal dimension of the hypocenters distribution. Also, the aftershocks obtained satisfy Omori’s law. Further,...