Abstract
We propose the use of a simple, cheap, and easy technique for the study of dynamic and synchronization of the coupled systems: effects of the magnetic coupling on the dynamics and of synchronization of two Colpitts oscillators (wireless interaction). We derive a smooth mathematical model to describe the dynamic system. The stability of the equilibrium states is investigated. The coupled system exhibits spectral characteristics such as chaos and hyperchaos in some parameter ranges of the coupling. The numerical exploration of the dynamics system reveals various bifurcations scenarios including period-doubling and interior crisis transitions to chaos. Moreover, various interesting dynamical phenomena such as transient chaos, coexistence of solution, and multistability (hysteresis) are observed when the magnetic coupling factor varies. Theoretical reasons for such phenomena are provided and experimentally confirmed with practical measurements in a wireless transfer.
Highlights
In electronics and in nonlinear dynamics, oscillators involving inductors are always modeled without any coupling from external magnetic field
We study the effect of the magnetic coupling on the behavior of a Colpitts coupled oscillator
The classical Colpitts oscillator is widely used in electronic devices and communication system as a source of sinusoidal waveform with low harmonic content [5]
Summary
In electronics and in nonlinear dynamics, oscillators involving inductors are always modeled without any coupling from external magnetic field. The synchronization of coupled chaotic systems has received a lot of attention since the early 1990s [1,2,3]. This has been motivated by potential application of chaotic signals in such areas as signal encryption and communications [4]. The classical Colpitts oscillator is widely used in electronic devices and communication system as a source of sinusoidal waveform with low harmonic content [5]. This oscillator has been extensively used in the investigation of various dynamical phenomena. The Colpitts oscillator is known to exhibit chaotic dynamics, it has been shown to exhibit an hyperchaotic behavior when coupled in various configurations [10, 11]
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