Energy Lyapunov function for generalized replicator equations

Replicator dynamics is an evolutionary strategy well established in different disciplines of biological sciences. It describes the evolution of self-reproducing entities called replicators in various independent models of, e.g., genetics, ecology, prebiotic evolution, and sociobiology. Besides this, replicator selection has been applied to problem solving in combinatorial optimization and to learning in neural networks and also in fluid mechanics, game and laser theory. So, the replicator systems arising in an extraordinary variety of modeling situations. In this paper the author introduces the new class of generalized replicator equations with nonlinear response functions and constructs an energy Lyapunov function for this system. Tsallis entropy is considered as an example.