Lag and anticipating synchronization without time-delay coupling

Abstract

We describe a new method for achieving approximate lag and anticipating synchronization in unidirectionally coupled chaotic oscillators. The method uses a specific parameter mismatch between the drive and response that is a first-order approximation to true time-delay coupling. As a result, an adjustable lag or anticipation effect can be achieved without the need for a variable delay line, making the method simpler and more economical to implement in many physical systems. We present a stability analysis, demonstrate the method numerically, and report experimental observation of the effect in radio-frequency electronic oscillators. In the circuit experiments, both lag and anticipation are controlled by tuning a single capacitor in the response oscillator.

Time shifts and correlations in synchronized chaos

“…This coupling produces a form of synchronization that approximates lag (anticipating) synchronization for suitably small positive (negative) values of the tuning parameter λ [6,7]. However, as the time shift is increased from zero (by increasing λ ), the amplitude of the response oscillator droops and the time shift eventually saturates.…”

“…This coupling was originally introduced as a method for obtaining time shifted synchronization without utilizing a true time delay [6,7]. However, as the lag or anticipation is increased from zero (by increasing λ ), the amplitude of the response oscillator droops and the lag or anticipation time saturates.…”

“…1(c). This circuit injects a current into the response oscillator proportional to the difference between Cx v , the voltage over the drive capacitor, and we therefore neglect it as long as λ is small [6,7]. The…”

“…Recently, some varieties of synchronization have been identified where the two trajectories are nearly but not exactly identical [2][3][4][5][6][7][8][9]. In these cases, either the coupling or a parameter mismatch produces a time-shifted synchronization state with some finite amplitude error.…”

Chaos suppression through asymmetric coupling

“…15,16 These latter forms of synchronization are being investigated for their potential technological applications. 17 Finally, a "generalized" synchronized state exists, where there is no equality of the two state variables but only a functional relation between them, 6,18…”