Asymmetric Chaos Research Articles

Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits. This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network (HNN) with coupled hyperbolic memristors through the modification of a single coupling connection weight. The bistable mode of the hyperbolic memristive HNN (mHNN), characterized by the coexistence of asymmetric chaos and periodic attractors, is effectively demonstrated through the utilization of conventional nonlinear analysis techniques. These techniques include bifurcation diagrams, two-parameter maximum Lyapunov exponent plots, local attractor basins, and phase trajectory diagrams. Moreover, an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors. This method demonstrates significant benefits in correlation, information entropy, and resistance to differential attacks, providing strong evidence for its effectiveness in encryption. Additionally, an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN. The correctness of the circuit design is confirmed through Multisim simulations, which align with numerical simulations conducted in Matlab.

Chaos induced by noise in a four-frequency ring gas laser

In a four-frequency class A ring gas laser with linear coupling of elliptically polarized counterpropagating waves, periodic regimes of lasing with oscillations of the intensity of one of the waves close to the threshold were revealed. Stochastization of these oscillations in the presence of a low-level δ-correlated white noise gives rise to the appearance of asymmetric chaos, evolving with a change in the detuning from the line center to symmetric chaos.

Quasi-synchronization phenomena in chaotic circuits coupled by one resistor

In this brief, synchronization phenomena observed from simple chaotic circuits coupled by one resistor are investigated. A simple three-dimensional autonomous circuit is considered as a chaotic sub-circuit. By carrying out circuit experiments and computer calculations for two, three or four subcircuits case, various interesting synchronization phenomena of chaos, which are different types from the results reported before, are confirmed to be stably generated. Further, quasi-synchronization of asymmetric chaos are investigated with attention on the number of synchronization states.

Symmetry-recovering crises of chaos in polarization-related optical bistability

We investigate delay-induced chaos in an optically bistable system which has a symmetry with respect to the exchange of two circular polarizations. Roughly speaking, the output of the system bifurcates in the following way as the input light intensity increases: (1) symmetric steady state, (2) asymmetric steady state, (3) asymmetric periodic oscillation, (4) asymmetric chaos, and (5) symmetric chaos. The first bifurcation is a well-known symmetry-breaking transition. It is shown that the last bifurcation through which the symmetry is recovered can be viewed as a crisis of chaos, which has been defined by Grebogi et al. as a sudden change of strange attractor. By changing system parameters, we find three distinct types of the crises in the experiment with an electronic circuit which simulates the difference-differntial system equation. Before and after the crises, waveforms characteristic of each type are observed. In a simple two-dimensional-map model, we can find all three types of crises. It is also found that the types of crises are determined by the nature of unstable fixed (or periodic) points which cause the crises by colliding with the chaotic attractors. The symmetry-recovering crises seem to be general phenomena appearing in nonlinear systems with some symmetries.