Chaos in a novel Wien bridge-based RC chaotic oscillator: dynamic analysis with application to image encryption

In the present contribution, we design a novel chaotic circuit with a symmetrical nonlinear component by replacing the single semiconductor diode in the original circuit by [Namajunas & Tamasevicius, 1995] with a pair of diodes connected in antiparallel. By exploiting the Shockley diode equation and adopting a judicious choice of state variables, we derive a smooth (i.e. with hyperbolic nonlinearities) mathematical model to investigate both the regular and chaotic dynamics of the novel RC oscillator. In addition to the familiar period-doubling bifurcations already observed in previous versions of the same oscillator, the novel oscillator exhibits more interesting dynamical properties including for instance, symmetry breaking bifurcation, merging crisis and coexisting multiple attractors as well. Interestingly, one of the most gratifying (and rare) features of the new circuit is the occurrence of both bubbles and reverse bubbles of bifurcation for some suitable parameter ranges. An excellent agreement is observed between theoretical and experimental results. The model is digitalized for digital image encryption. First the Hahn orthogonal moments of each pixel of the plain image is computed, and then Knuth permutation algorithm is combined to chaotic sequences to scramble the resulting image in the transform domain. Finally, the permuted image will be diffused using the pseudo random chaotic sequences. Security analysis indicates good performances of the model to encrypt and decrypt digital images.

Automated summary

In this paper, a novel chaotic circuit is designed and its regular and chaotic dynamics are investigated using a mathematical model. The circuit exhibits interesting dynamical properties and is successfully applied to digital image encryption.