Phase Retrieval and Reconstruction of Coherent Synthesis by Genetic Algorithm

In the context of diffractive optics, phase retrieval is a heavily investigated process of recreating an entire complex electric field from partial amplitude-only information through iterative algorithms. However, existing methods can fall into local minima during reconstructions or struggle to recover unusual and novel electric field distributions. We present a numerical method based on a global-optimization genetic algorithm that reconstructs non-trivial electric field distributions from single diffracted intensity distributions. Diffraction and propagation of the optical fields over arbitrary distances is modeled through implementation of the angular spectrum technique. Additionally, a coherently-locked laser array system is used as an experimental case-study demonstrating $0.09 \pi$ phase reconstruction accuracy of initial laser parameters from single intensity images.

A 2D Hyperchaotic Map: Amplitude Control, Coexisting Symmetrical Attractors and Circuit Implementation

An absolute value function was introduced for chaos construction, where hyperchaotic oscillation was found with amplitude rescaling. The nonlinear absolute term brings the convenience for amplitude control. Two regimes of amplitude control including total and partial amplitude control are discussed, where the attractor can be rescaled separately by two independent coefficients. Symmetrical pairs of coexisting attractors are captured by corresponding initial conditions. Circuit implementation by the platform STM32 is consistent with the numerical exploration and the theoretical observation. This finding is helpful for promoting discrete map application, where amplitude control is realized in an easy way and coexisting symmetrical sequences with opposite polarity are obtained.

Synchronization patterns: from network motifs to hierarchical networks

We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart–Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is motivated by the network of neurons in the brain. This fractal property is well represented in hierarchical networks, for which we present three different models. In addition, we introduce an analytical eigensolution method and provide a comprehensive picture of the interplay of network topology and the corresponding network dynamics, thus allowing us to predict the dynamics of arbitrarily large hierarchical networks simply by analysing small network motifs. We also show that oscillation death can be induced in these networks, even if the coupling is symmetric, contrary to previous understanding of oscillation death. Our results show that there is a direct correlation between topology and dynamics: hierarchical networks exhibit the corresponding hierarchical dynamics. This helps bridge the gap between mesoscale motifs and macroscopic networks. This article is part of the themed issue ‘Horizons of cybernetical physics’.

Crisis in Amplitude Control Hides in Multistability

A crisis of amplitude control can occur when a system is multistable. This paper proposes a new chaotic system with a line of equilibria to demonstrate the threat to amplitude control from multistability. The new symmetric system has two coefficients for amplitude control, one of which is a partial amplitude controller, while the other is a total amplitude controller that simultaneously controls the frequency. The amplitude parameter rescales the basins of attraction and triggers a state switch among different states resulting in a failure of amplitude control to the desired state.

Experimental Implementation of Networked Chaotic Oscillators Based on Cross-Coupled Inverter Rings in a CMOS Integrated Circuit

A novel chaotic oscillator based on "cross-coupled" inverter rings is presented. The oscillator consists of a 3-ring to which higher odd n-rings are progressively coupled via diodes and pass gates; it does not contain reactive or resistive elements, and is thus suitable for area-efficient implementation on a CMOS integrated circuit. Numerical simulation based on piece-wise linear approximation predicted the generation of positive spikes having approximately constant periodicity but highly variable cycle amplitude. Simulation Program with Integrated Circuit Emphasis (SPICE) simulations and experimental data from a prototype realized on 0.7 μm technology confirmed this finding, and demonstrated increasing correlation dimension (D2) as 5-, 7- and 9-rings were progressively coupled to the 3-ring. Experimental data from a ring of 24 such oscillator cells showed phase synchronization and partial amplitude synchronization (formation of small clusters), emerging depending on DC gate voltage applied at NMOS transistors implementing diffusive coupling between neighboring cells. Thanks to its small area, simple synchronizability and digital controllability, the proposed circuit enables experimental investigation of dynamical complexity in large networks of coupled chaotic oscillators, and may additionally be suitable for applications such as broadband signal and random number generation.

Response Sensitivity and the Assessment of Nonlinear Vibration Using a Nonlinear Lateral–Torsional Coupling Model of Vehicle Transmission System

The eigensensitivity analysis does not meet the increasing industrial requirements of the dynamic performance of a vehicle transmission system. To reduce vibration, it is necessary to include response sensitivity in the guideline in the design stage. In this study, we developed a nonlinear lateral–torsional coupling spur gear system model considering the effect of time-varying mesh stiffness, clearance, mass eccentricity, and transmission error. Then the dynamic response sensitivity to system parameters was systematically analyzed by taking the shaft torsional stiffness, for example. The equation of response sensitivity was deduced by a direct method (DM) based on the fitting of the clearance function curve using a polynomial function. In allusion to the characteristic of the aperiodicity of response sensitivity curves of the nonlinear system in the time domain, a novel assessment method—differential sensitivity based on the root mean square (RMS) of response is proposed. This method provides statistical results in a certain range, thus avoiding the inaccuracy of the partial amplitude. The vibrational energy of modified system (MS) can also be estimated. All the abovementioned characteristics make it possible to provide the theoretical support for dynamic modification, model updating, and optimal design.