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A feedback control method is proposed to create a degenerate Hopf bifurcation in three-dimensional maps at a desired parameter point. The particularity of this bifurcation is that the system admits a stable fixed point inside a stable Hopf circle, between which an unstable Hopf circle resides. The interest of this solution structure is that the asymptotic(More)
Projective synchronization (PS), in which the state vectors synchronize up to a scaling factor, is usually observable only in partially linear systems. We show that PS could, by means of control, be extended to general classes of chaotic systems with nonpartial linearity. Performance of PS may also be manipulated by controlling the scaling factor to any(More)
The ultimate state of projective synchronization is hardly predictable. A control algorithm is thus proposed to manipulate the synchronization in arbitrary dimension. The control law derived from the Lyapunov stability theory with the aid of slack variables is effective to any initial conditions. The method allows us to amplify and reduce the synchronized(More)
Tracing back to the initial state of a time-evolutionary process using a segment of historical time series may lead to many meaningful applications. In this paper, we present an estimation method that can detect the initial conditions, unobserved time-varying states and parameters of a dynamical (chaotic) system using a short scalar time series that may be(More)
This report presents a technique of chaotification based on the optimal time-delay feedback that can make a system chaotic with large chaotic parameters range. The bifurcation analysis is done to determine the stability of the time-delay system. An implicit performance index and an optimization strategy are proposed for the time-delay control scheme that(More)