Theoretical study and circuit implementation of three chain-coupled self-driven Duffing oscillators.

In this paper, we describe the scenario from the birth of oscillations to multi-spiral chaos in a novel system composed of three chain-coupled self-driven Duffing oscillators. Eight of the equilibrium points develop (multiple) Hopf bifurcation when varying a parameter (e.g., coupling coefficient). Considering the computer integration of the state equations, the combined exploitation of Lyapunov exponent plots, bifurcation diagrams, basins of attraction, and phase portraits, unusual and attractive features were highlighted including the coexistence of eight bifurcation branches, Hopf bifurcations, a multitude of coexisting types of oscillations and a six-spiral chaotic attractor, just to cite a few. Using basic electronic components, the electronic circuit of the three chain-coupled Duffing oscillator system is performed. Orcad-PSpice simulated dynamics of the proposed chain-coupled analog circuit confirm the theoretically disclosed features. Moreover, the practical feasibility of the coupled system is demonstrated by considering microcontroller-based hardware realization.

Nonlinear dynamics in an optoelectronic feedback delay oscillator with piecewise linear transfer functions from the laser diode and photodiode.

We investigate the nonlinear dynamics of a recent architecture of an optoelectronic oscillator, where the emitting laser and the receiving diode are connected in a head-to-tail configuration via an optical fiber delay line. The resulting nonlinear transfer function is a piecewise linear profile, and its interplay with the delay leads to many complex behaviors such as relaxation oscillations and deterministic chaos. This system belongs to a recent class of optoelectronic oscillators where the nonlinearity does not originate from the sinusoidal transfer function of an imbalanced interferometer, and, in particular, it is a simple optoelectronic oscillator configuration that is capable of displaying a chaotic behavior. The results of the analytic study are confirmed by numerical simulations and experimental measurements.

A Multidimensional Hyperjerk Oscillator: Dynamics Analysis, Analogue and Embedded Systems Implementation, and Its Application as a Cryptosystem.

A lightweight image encryption algorithm is presented based on chaos induction via a 5-dimensional hyperjerk oscillator (5DHO) network. First, the dynamics of our 5DHO network is investigated and shown to exhibit up to five coexisting hidden attractors in the state space that depend exclusively on the system's initial values. Further, a simple implementation of the circuit was used to validate its ability to exhibit chaotic dynamical properties. Second, an Arduino UNO platform is used to confirm the usability of our oscillator in embedded system implementation. Finally, an efficient image encryption application is executed using the proposed chaotic networks based on the use of permutation-substitution sequences. The superior qualities of the proposed strategy are traced to the dynamic set of keys used in the substitution process which heralds the generation of the final ciphered image. Based on the average results obtained from the entropy analysis (7.9976), NPCR values (99.62), UACI tests (33.69) and encryption execution time for 512 × 512 images (0.1141 s), the proposed algorithm is adjudged to be fast and robust to differential and statistical attacks relative to similar approaches.