Sensitivity, Roughness and Bifurcations of Dynamic Systems

Questions of sensitivity, roughness and bifurcation of systems at parametrical perturbations are considered. Stages of development of the theory of sensitivity, the theory of a robustness and the theory of roughness and also the theory of bifurcation of dynamic systems are given. Basic provisions of the theory and method of topological roughness of systems are stated, which based on a concept of roughness according to Andronov-Pontryagin is considered. The method allows to research roughness (robustness) and bifurcations of dynamic systems of various nature, in particular synergetic systems and also to synthesize rough (robust) control systems, through control of roughness.