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Complex Dynamics and Bifurcation in a Two-Ring System With Phase Control

Modes of dynamic behavior in a coupled system with phase and time-delay control are studied. The sys-tem is intended for tracking estimation of a complex signal’s parameters. The case is considered when one of the subsystems individually demonstrates simple regular dynamics while the other subsystem exhibits both regu-lar and chaotic dynamical states. The behavior of the examined system is described by nonlinear fore-dimensional set of differential equations with periodical nonlinearity. The bifurcation diagram is determined, the regions with the state of phase synchronization, periodic and chaotic nonsynchronous modes of interacting sub-systems are found. Scenarios of development of non-synchronous modes under variation of the system pa-rameters are established. The possibilities of control over properties and domains of existence of dynamical regimes are ascertained by varying of system’s parame-ters values.
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