Chua’s Circuit with Time-Depended Variable Capacitances and Its Synchronization

The paper deals with the study of the parametrically driven Chua’s circuit. We use Lagrangian formalism together with Kirchhoff rules to perform modeling of parametrically driven Chua’s circuit. Such an approach allows us to represent the dynamic of Chua’s circuit by different state variables. This dynamic is described by differential equations in general form for some time-depended boundary functions, which describe the changing of capacitances. Thus, we define a general model for parametrically driven Chua’s circuit. Then this model is used to study Chua’s circuit dynamic with harmonically changed capacitors. We use numerical methods to solve differential equations of modified Chua’s circuit and prove its difference from classical Chua’s circuit. This difference is proven in time and frequency domains. Our studies show that chaotic oscillations in modified Chua’s circuit are nonlinear ones in the time domain and they have high-frequency harmonics in its harmonic spectrum. We plot 3D attractors of modified and classical Chua’s circuits, which prove circuits’ difference as well. We offer to avoid considering nonlinear functions while the synchronization controller is being designed by using minimal and maximal values of these functions only and constructing an interval model for Chua’s circuit. Combination of this model and feedback linearization methods allows us to design a simple sliding mode feedback controller, which transform the dynamic of Chua’s circuit into Brunovsky form. We use the simplest first order sliding mode controller in the control system feedforward to perform synchronization of the transformed object’s dynamic with an external signal.