Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

SEARCH GUIDE  Download Search Tip PDF File

  • articleNo Access

    TRACKING PHASE SYNCHRONIZATION OF TWO COUPLED RÖSSLER OSCILLATORS WITH INTERNAL RESONANCE

    Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, we tune the linear coupling parameter to obtain the two Rössler oscillators in a synchronized regime and analyze the effect of a nonlinear coupling on the phase synchronized state. It demonstrates that the detuning parameter σ between the two natural frequencies ω1 and ω2 affects phase dynamics, and with the increase of the nonlinear coupling strength, for the primary resonance, the effect of phase synchronization between two sub-systems was decayed, while increasing with frequency ratio 1:2. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the nonlinear coupling strength.

  • articleNo Access

    PHASE SYNCHRONIZATION OF RÖSSLER OSCILLATORS WITH PARAMETRIC EXCITATION

    Phase synchronization of parametric excited Rössler system has been investigated in this paper. By introducing the conception of phase for a chaotic motion, it has been demonstrated that the mean frequency of chaotic attractor and the frequency of the parametric excitation may be locked in different ratios for certain parameter conditions, implying phase synchronization can be observed. The evolution from nonsynchronized state to phase synchronization has been discussed in detail, which reveals different phase dynamics may exist during the process. With the variation of parameters, the imaging point on the Poincaré plane may finally settle down onto the attractor, which yields phase synchronization.

  • articleNo Access

    CHAOTIC DYNAMICS OF A SPATIO-INHOMOGENEOUS MEDIUM

    In the present paper we show that inhomogeneity of a continuous self-sustained oscillating medium can be a reason for the onset of chaotic behavior. It has been established that temporal chaotic dynamics typically arises in the medium with a linear mismatch of the natural frequency along a spatial coordinate, whereas a chaotic regime is not characteristic for the medium with randomly distributed frequencies. The interconnection has been revealed between the temporal chaotic behavior and the spatial formation of imperfect clusters. The spectral and correlation analysis as well as the linear analysis of stability of regular and chaotic regimes in the inhomogeneous medium are performed. The correlation of the instantaneous phase dynamics of oscillations with the behavior of autocorrelation functions has been examined. It has been established that the characteristics of temporal chaos correspond to a spiral attractor (Shilnikov's attractor).

  • articleNo Access

    INSTANTANEOUS PHASE METHOD IN STUDYING CHAOTIC AND STOCHASTIC OSCILLATIONS AND ITS LIMITATIONS

    We study the behavior of an instantaneous phase and mean frequency of chaotic self-sustained oscillations and noise-induced stochastic oscillations. The results obtained by using various methods of the phase definition are compared to each other. We also compare two methods for describing synchronization of chaotic self-sustained oscillations, namely, instantaneous phase locking and locking of characteristic frequencies in power spectra. It is shown that the technique for diagnostics of the chaos synchronization based on the instantaneous phase locking is not universal.