Chaotic function generator: complex dynamics and its control in a loss-modulated Nd:YAG laser

Modeling of a multi-parameter chaotic optoelectronic oscillator based on the Fourier neural operator

A model construction scheme of chaotic optoelectronic oscillator (OEO) based on the Fourier neural operator (FNO) is proposed. Different from the conventional methods, we learn the nonlinear dynamics of OEO (actual components) in a data-driven way, expecting to obtain a multi-parameter OEO model for generating chaotic carrier with high-efficiency and low-cost. FNO is a deep learning architecture which utilizes neural network as a parameter structure to learn the trajectory of the family of equations from training data. With the assistance of FNO, the nonlinear dynamics of OEO characterized by differential delay equation can be modeled easily. In this work, the maximal Lyapunov exponent is applied to judge whether these time series have chaotic behavior, and the Pearson correlation coefficient (PCC) is introduced to evaluate the modeling performance. Compare with long and short-term memory (LSTM), FNO is not only superior to LSTM in modeling accuracy, but also requires less training data. Subsequently, we analyze the modeling performance of FNO under different feedback gains and time delays. Both numerical and experimental results show that the PCC can be greater than 0.99 in the case of low feedback gain. Next, we further analyze the influence of different system oscillation frequencies, and the generalization ability of FNO is also analyzed.

Broadband chaos generated by an optoelectronic oscillator

We study an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. We derive approximate mappings that do an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks.

Chaotic dynamics and synchronization in microchip solid-state lasers with optoelectronic feedback

We experimentally observe the dynamics of a two-mode Nd:YVO4 microchip solid-state laser with optoelectronic feedback. The total laser output is detected and fed back to the injection current of the laser diode for pumping. Chaotic oscillations are observed in the microchip laser with optoelectronic self-feedback. We also observe the dynamics of two microchip lasers coupled mutually with optoelectronic link. The output of one laser is detected by a photodiode and the electronic signal converted from the laser output is sent to the pumping of the other laser. Chaotic fluctuation of the laser output is observed when the relaxation oscillation frequency is close to each other between the two microchip lasers. Synchronization of periodic wave form is also obtained when the microchip lasers have a single-longitudinal mode.

A programmable electronic circuit for modelling CO2 laser dynamics

We introduce a programmable electronic circuit implementing the rich dynamics of CO2 laser models. The design and the implementation of the circuit are accomplished by using a programmable analog device, which permits an experimental characterization of the laser dynamics. The experimental results shown in the paper demonstrate that the circuit exhibits homoclinic chaos typical of CO2 laser with feedback modulation of cavity losses. Moreover, experimental results showing that noise regularizes the dynamical time scales of the system are reported.

Coherence in scale-free networks of chaotic maps

We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) a random scale-free topology, (ii) a deterministic pseudofractal scale-free network, and (iii) an Apollonian network. For the random scale-free topology we find a coupling strength threshold beyond which full synchronization is attained. This threshold scales as k(-mu) , where k is the outgoing connectivity and mu depends on the local nonlinearity. For deterministic scale-free networks coherence is observed only when the coupling strength is proportional to the neighbor connectivity. We show that the transition to coherence is of first order and study the role of the most connected nodes in the collective dynamics of oscillators in scale-free networks.

Adaptive control of unknown unstable steady states of dynamical systems

A simple adaptive controller based on a low-pass filter to stabilize unstable steady states of dynamical systems is considered. The controller is reference-free; it does not require knowledge of the location of the fixed point in the phase space. A topological limitation similar to that of the delayed feedback controller is discussed. We show that the saddle-type steady states cannot be stabilized by using the conventional low-pass filter. The limitation can be overcome by using an unstable low-pass filter. The use of the controller is demonstrated for several physical models, including the pendulum driven by a constant torque, the Lorenz system, and an electrochemical oscillator. Linear and nonlinear analyses of the models are performed and the problem of the basins of attraction of the stabilized steady states is discussed. The robustness of the controller is demonstrated in experiments and numerical simulations with an electrochemical oscillator, the dissolution of nickel in sulfuric acid; a comparison of the effect of using direct and indirect variables in the control is made. With the use of the controller, all unstable phase-space objects are successfully reconstructed experimentally.

Generalized synchronization of chaos in identical systems with hidden degrees of freedom

We demonstrate generalized synchronization of chaos in a two-mode laser system. The total intensity of the laser output (the sum of the individual mode intensities) is used as the drive signal. This lumped variable transmitted to the identical response system does not generate identical synchronization. Generalized synchronization is observed instead of identical synchronization because of the hidden internal degrees of freedom.

Competition between two frequencies for phase synchronization of a chaotic laser

Competition between two distinct driving frequencies to phase synchronize the intensity dynamics of a chaotic laser has been observed. The phase of the chaotic intensity signal is constructed using the complex analytic signal. Competing frequencies alternately show phase locking and phase slipping. Competition has been quantified by calculating the portion of time the laser phase locks to each of the driving frequencies and their average.