Frequency–driven chaos in the electrical circuit of Duffing-Holmes oscillator and its control

Accurate detection of weak periodic signals within noise and possibility of secure messaging have made Duffing oscillator (DO) highly important in the field of communication. Investigation on the properties of DO is thus ardently sought for. An elegant approach to accomplish the same is to fabricate electronic circuit simulating DO non-linear equation and to study the effect of input signal amplitude (Vin) and frequency (f), disentangling each other.   Recently, Vin-driven chaotic dynamics was studied by constructing a simple Duffing-Holmes (DH) oscillator circuit. However, the f-driven characteristics of the oscillator remain unknown at constant Vin. The present work is based on the MATLAB simulation of f-driven chaotic dynamics of the DH equation. Similar output, mixed with chaos and non-chaos, is obtained by constructing the circuit, both in lab and PSPICE simulation. The circuit moves into complete chaos at f=270 Hz, while period-2 bifurcation appears at f=680 Hz for constant Vin 0.9V.  The chaos control is also achieved by two simple methods. In the first method, the variation of circuit parameter (capacitance) induces chaos control. In the second method, synchronization is achieved by coupling two similar oscillators. These two methods, though apparently simple, could be highly beneficial for using DH in secure communication.