Hybrid Chaos Synchronization of 3-Cells Cellular Neural Network Attractors via Adaptive Control Method

Abstract: In this research work, we first discuss the properties of the 3-cells cellular neural network (CNN) attractor discovered b

Hybrid Synchronization of the Generalized Lotka-Volterra Three-Species Biological Systems via Adaptive Control

Abstract: Since the recent research has shown the importance of biological control in many biological systems appearing in nature, this research paper investigates research in the dynamic and chaotic analysis of the generalized Lotka-Volterra three-species biological system, which was studied b

Finite-Time Synchronization of the Rabinovich and Rabinovich-Fabrikant Chaotic Systems for Different Evolvable Parameters

This paper addresses the challenge of synchronizing the dynamics of two distinct 3D chaotic systems, specifically the Rabinovich and Rabinovich-Fabrikant systems, employing a finite-time synchronization approach. These chaotic systems exhibit diverse characteristics and evolving chaotic attractors, influenced by specific parameters and initial conditions. Our proposed low-cost finite-time synchronization method leverages the signum function's tracking properties to facilitate controlled coupling within a finite time frame. The design of finite-time control laws is rooted in Lyapunov stability criteria and lemmas. Numerical experiments conducted within the MATLAB simulation environment demonstrate the successful asymptotic synchronization of the master and slave systems within finite time. To assess the global robustness of our control scheme, we applied it across various system parameters and initial conditions. Remarkably, our results reveal consistent synchronization times and dynamics across these different scenarios. In summary, this study presents a finite-time synchronization solution for non-identical 3D chaotic systems, showcasing the potential for robust and reliable synchronization under varying conditions

Adaptive self-recurrent wavelet neural network and sliding mode controller/observer for a slider crank mechanism

In this paper, a novel control strategy based on an adaptive Self-Recurrent Wavelet Neural Network (SRWNN) and a sliding mode controller/observer for a slider crank mechanism is proposed. The aim is to reduce the tracking error of the linear displacement of this mechanism while following a specified trajectory. The controller design consists of two parts. The first one is a sliding mode control strategy and the second part is an SRWNN controller. This controller is trained offline first, and then the SRWNN weights are updated online by the adaptive control law. Apart from the hybrid control strategy proposed in this paper, a velocity observer is implemented to replace the use of velocity sensors. The outcomes obtained in the numerical experiment section prove that the smallest tracking error is obtained for the linear and angular displacements in comparison with other strategies found in literature due to the uncertainty and disturbance rejection properties of the sliding mode and the self-recurrent wavelet neural network controllers.Peer ReviewedPostprint (author's final draft

A new fractional-order chaotic system with its analysis, synchronization, and circuit realization for secure communication applications

YesThis article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the sug-gested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Nonlinear data assimilation using synchronisation in a particle filter

Current data assimilation methodologies still face problems in strongly nonlinear systems. Particle filters are a promising solution, providing a representation of the model probability density function (pdf) by a discrete set of particles. To allow a particle filter to work in high-dimensional systems, the proposal density freedom is a useful tool to be explored. A potential choice of proposal density might come from the synchronisation theory, in which one tries to synchronise the model with the true evolution of a system using one-way coupling, via the observations, by adding an extra term to the model equations that will control the growth of instabilities transversal to the synchronisation manifold. Efficient synchronisation is possible in low-dimensional systems, but these schemes are not well suited for high-dimensional settings. The first part of this thesis introduces a new scheme: the ensemble-based synchronisation, that can handle high-dimensional systems. A detailed description of the formulation is presented and extensive experiments in the nonlinear Lorenz96 model are performed. Successful results are obtained and an analysis of the usefulness of the scheme is made, bringing inspiration for a powerful combination with a particle filter. In the second part, the ensemble synhronisation scheme is used as a proposal density in two different particle filters: the Implicit Equal-Weights Particle Filter and the Equivalent-Weights Particle Filter. Both methodologies avoid filter degeneracy by construction. The formulation proposed and its implementation are described in detail. Tests using the Lorenz96 model for a 1000-dimensional system show qualitatively reasonable results, where particles follow the truth, both for observed and unobserved variables. Further tests in the 2-D barotropic vorticity model were also performed for a grid of up to 16,384 variables, also showing successful results, where the estimated errors are consistent with the true errors. The behavior of the two schemes is described and their advantages and issues exposed, as this is the first comparison ever made between both filters. The overall message is that results suggest that the combination of the ensemble synchronisation with a particle filter is a promising solution for high-dimensional nonlinear problems in the geosciences, connecting the synchronisation field to data assimilation in a very direct way

Synchronization and application of delay-coupled semiconductor lasers

The work in this thesis is focused on the complex dynamics of semiconductor laser (SL) devices which receive time-delayed feedback from an external cavity or are delay-coupled with a second semiconductor laser. We investigate fundamental properties of the dynamics and study the utilization of transient complex dynamics of a single SL arising from delayed feedback and external signal injection for a neuro-inspired photonic data processing scheme. Based on experiments and numerical modelling, we investigate systems of two coupled SLs, gaining insights into the role of laser and coupling parameters for the synchronization characteristics of these systems. We link certain features of the synchronization dynamics, like intermittent desynchronization events, to the underlying nonlinear dynamics in the coupled laser system. Our research thus combines both fundamental insights into delay-coupled lasers as well as novel application perspectives