Universal approach to the problem of emergence of chaos in autonomous dynamical systems

A new method for studying the problem of emergence of chaos in dynamical systems, the right-hand sides of which are continuously differentiable functions, is proposed. The application of obtained results to the investigation of chaotic dynamical systems without homoclinic or heteroclinic orbits and also without use of the concept of equilibrium points (for example, it can be memristive systems) is shown. In addition, the offered method can be used as a tool for search of hidden chaotic attractors.