An approach combining periodicity ratio and secondary Poincare, map for characteristics diagnosis of nonlinear oscillatory systems

A secondary Poincar, map approach is developed in this research for diagnosing the nonlinear characteristics such as quasiperiodic and chaotic responses of a dynamic system. With the secondary Poincar, map approach developed, an approach combining the periodicity ratio method and the secondary Poincar, map approach is established such that all the dynamical characteristics of a nonlinear dynamic system can be systemically and completely identified. An example of an ecological oscillatory system is presented in the research to demonstrate the application of the combined approach. Periodic-quasiperiodic-chaotic region diagrams are generated with the employment of the approach, for a global characterization of this system with consideration of large ranges of system parameters. The approach developed in this research demonstrates effectiveness and efficiency in completely diagnosing the complex dynamical characteristics of nonlinear oscillatory systems, such as periodic, quasiperiodic, chaotic responses of the systems together with those in between periodic and chaotic responses.