We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differentialdifference equations, difference equations and cellular automata (ultra-discrete equations).

in this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (nsfds). numerical examples confirming then efficiency of schemes, for some differential equations are provided. in order toillustrate the accuracy of the new nsfds, the numerical results are compared with s...

The present study focuses on a class of games with reinforcement-learning agents that adaptively choose their actions to locally maximize their rewards. By analyzing a limit model with a special type of learning, previous studies suggested that dynamics of games with learners may become chaotic. We evaluated the generality of this model by analyzing the consistency of this limit model in compar...

Integrable difference equations commonly have more low-order conservation laws than occur for non-integrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in order to find candidates for integrability. It turns out that all such candidates have an equivalent affine form. These are tested by calculating their algebrai...