Coupled Chaotic Colpitts Oscillators: Identical and Mismatched Cases

Abstract

A system consisting of two linearly coupled chaotic Colpitts oscillators is considered. Two different coupling configurations, namely coupled collector nodes (C-C) and coupled emitter nodes (E-E) have been investigated. In addition to identical oscillators the case of mismatched circuits has been studied. Specifically the influence of the transistor parameter mismatch has been analyzed. The relative synchronization error has been estimated for different mismatch levels provided the coupling coefficient is twice larger than the synchronization threshold. Illustrative experimental results, including phase portraits and synchronization error are presented.

Particle Filter-Based Synchronization of Chaotic Colpitts Circuits Combating AWGN Channel Distortion

“…To evaluate the estimation performance, namely the synchronization performance, we define the synchronization error E and average attractor distance (AAD) D: [1] 2 + e k [2] 2 + e k [3] 2 (13)…”

“…Under ideal synchronization conditions, mathematical analysis and simulation results have confirmed that perfect synchronization can be achieved when no parameter mismatches and channel distortions are considered [10,14,15,17,19]. In the experimental studies of this synchronization problem, parameter mismatches, including the discrete components (resistors, capacitors, inductors) and the transistor parameter mismatches, are considered, and it was found that with minor parameter mismatches, chaos synchronization can still be obtained and maintained [2,3,23]. Recently, a nonlinear observer-based synchronization scheme for a Colpitts oscillator has been investigated [5], where all parameters of a totally uncertain model of the oscillator can be estimated through parameter identification, and it offers a potentially promising way to combat parameter mismatches.…”

Full- and reduced-order synchronization of a class of time-varying systems containing uncertainties

“…Now, the aim is to design an adaptive controller u to synchronize system (2) with system (9). Viewing the error system (11), the controller can be chosen…”

“…Complete synchronization (CS) has been shown to occur in structurally equivalent dynamical systems, i.e., either identical systems [9] or systems in which the nonidentity results in a rather slight parameter mismatch [10], as well as in strictly different dynamical systems, i.e., systems with different model structures [11] involving different order [12].…”

Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control

“…The synchronization of chaotic Colpitts oscillators was studied in several works [18,[20][21][22][23][24][25]. To synchronize Colpitts oscillators, either nonlinear Pecora-Caroll method [21,22] or linear coupling technique [18,20,25], adaptive synchronization [24], active control synchronization [23], linear feedback control method [26] have been employed. Recently, we studied the synchronization of the improved and standard versions of the Colpitts oscillator with different orders and we proposed a controller based on the stability theory by constructing progressively the Lyapunov function to ensure chaos synchronization of both oscillators [27].…”