Replicator equations, response functions and entropy measures in science: mathematical background

摘要

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 arise in an extraordinary variety of modeling situations. In this report we'll consider the new class of generalized replicator equations with nonlinear response functions and construct the Energy Lyapunov function and entropy measures for this system.