Generation of Homoclinic Oscillation in the Phase Synchronization Regime in Coupled Chua's Oscillators

Abstract

An experimental method for generating homoclinic oscillations using two nonidentical Chua's oscillators coupled in unidirectional mode is described here. A homoclinic oscillation is obtained at the response oscillator in the weaker coupling limit of phase synchronization. Different phase locking phenomena of homoclinic oscillations with external periodic pulse have been observed when the frequency of the pulse is close to the natural frequency of the homoclinic oscillation or its subharmonics.

Homoclinic bifurcation in Chua’s circuit

“…where G = 1/R 1 and G a , G b are the slopes in the inner and outer regions [21][22][23] respectively of the piece-wise linear characteristic f (V C1 ). The slopes G a and G b are determined by…”

“…To facilitate fine control over the strength of asymmetry, a series resistance R C is connected between the voltage divider and the Chua's circuit. The symmetric Chua's circuit (no DC forcing) shows [21][22][23] transition from limit cycle to single scroll chaos via PD and then to alternate period adding and chaotic states via saddle-node (SN) and PD bifurcation respectively, and finally to double scroll chaos. The original model has three saddle foci, one near the origin with eigenvalues (γ, −σ ± jω) and other two at reflection symmetric positions with eigenvalues (−γ, σ ± jω).…”