By Ricardo Femat, Gualberto Solis-Perales
This pages comprise the consequences derived in the course of final ten years approximately either suppression and synchronization of chaotic -continuous time- platforms. alongside this time, our inspiration used to be to check how the intrinsic houses of dynamical structures could be exploited to suppress and to synchronize the chaotic habit and what synchronization phen- ena are available lower than suggestions interconnection. Our findings have brought on shock to us and feature influenced our surprising power. might be, reader can think our faces with opens eyes like young ones seeing round items; that are in all likelihood noticeable for others and novel for us. A compilation of our surprises approximately those findings is being defined alongside this ebook. e-book comprises either targets to proportion our ama- ment and to teach our point of view on synchronization of chaotic platforms. therefore, whereas we have been writing the preface, we mentioned its scope. considering as a booklet readers, we discovered preface should still resolution, in few phrases, the subsequent query: What can the reader locate during this book?, reader can locate our steps towards realizing of c- otic habit and the opportunity of suppressing and synchronizing it. We to begin with exhibit the chaos suppression shape experimental area to capability implementation in excessive tech method as a levitation method in response to extreme temperature Superconductors (HTS). This bankruptcy is used as departing aspect in the direction of a extra advanced challenge the chaotic synchronization. Then, reader travels through the synchronization of the chaotic habit global all through precise suggestions approaches.
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Additional resources for Robust Synchronization of Chaotic Systems via Feedback
Moreover, in spite of the control command only affects x1; x2, and x3 display regular behavior. 14) via the PII2 controller. Such synchronization is achieved by tracking the reference r(t). That is, the time function r(t) is yielded by a reference system (which can be so-called drive system); then under closed-loop, the output of the response system tracks the reference signal. 14). In some manner if the driven system can be chosen as a chaotic system, the output of the response system should track the reference signal.
Mex. Fis. : A generic input-output analysis of zerodispersion noninear resonance. Europhys. Letts. : Suppression of chaos by resonant parametric perturbation. Phys. Rev. : Chaos in dynamical systems. : Dynamical chaos: models and experiments. : Stochastic resonance in chaotic laser. Phys. Rev. : Model reference control of regular and chaotic dynamics in the Duffing-Ueda oscillator. IEEE Trans. Circ. & Syst. : Continuous control of chaos by self-controlling feedback. Phys. Lett. : Modal feedback control on chaotic trajectories.
9) to the prescribed reference (z*,w*) in face of lack of knowledge if the initial condition satisfies (z(0),w(0), (0)) = 0. In fact, the feedback control u = - [ + k(z - z*)]/ = - [ (z) + k(z - z*)]/ due to by definition, = (z). 9) has a relative degree, = 1, the new state is not available for feedback. Indeed, it cannot be measured because it is an intermediate variable toward the final controller which defines the dynamical behavior of the uncertain vector field f(x). 12. 9) asymptotically to the prescribed reference (z*,w*).