Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders

The precise anti-synchronization control of uncertain chaotic systems has always remained an interesting problem. The anti-synchronization control of multiple different orders uncertain chaotic systems increases the complexity and enhances the security of the information signal in secure communications. Hence, it confines the hacking in digital communication systems. This paper proposes a novel adaptive control technique and studies the double combination anti-synchronization of multiple different orders uncertain chaotic systems. The proposed adaptive feedback control technique consists of three fundamental nonlinear components. Each component accomplishes a different objective; (i) stability of the closed-loop, (ii) smooth and fast convergence behaviour of the anti-synchronization error, and (iii) disturbance rejection. The theoretical analysis in (i) to (iii) uses the Lyapunov stability theory. This paper also provides parameters adaptation laws that stabilize the uncertain parameters to some constants. The paper discusses the simulation results of two representative examples of four different orders uncertain chaotic systems. These examples demonstrate anti-synchronization among hyperchaotic Lü, uncertain chaotic Shimizu Morioka, uncertain second-order nonlinear duffing, and uncertain parametrically excited second-order nonlinear pendulum systems. The computer-based simulation results certify the efficiency and performance of the proposed anti-synchronization control approach and compare them with peer works

Analysis of a class of complex system without equilibria via switched control law

"In this article we introduce a new class of complex system without equilibria which exhibits a chaotic multiscroll attractor in each node. The number of scrolls in the attractor is determined by a switched control law to allow the operation of different linear affine systems. Thus, the system is composed of many subsystems which interact with each other to generate a multiscroll attractor. This new class of piecewise linear (PWL) system presents no positive real part in the eigenvalues of the Jacobian matrix as opposed to the reported systems with multiscrolls. The scrolls present a complex behavior since these don’t unwrap and don’t appear close to an unstable manifold of a saddle-focus equilibrium point. A particular case is taken as case study and simulation plots of the attractor are provided.

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Dissipative Solitons in Fibre Lasers

Interdisciplinary concept of dissipative soliton is unfolded in connection with ultrafast fibre lasers. The different mode-locking techniques as well as experimental realizations of dissipative soliton fibre lasers are surveyed briefly with an emphasis on their energy scalability. Basic topics of the dissipative soliton theory are elucidated in connection with concepts of energy scalability and stability. It is shown that the parametric space of dissipative soliton has reduced dimension and comparatively simple structure that simplifies the analysis and optimization of ultrafast fibre lasers. The main destabilization scenarios are described and the limits of energy scalability are connected with impact of optical turbulence and stimulated Raman scattering. The fast and slow dynamics of vector dissipative solitons are exposed

Nonlinear Dynamics of Semiconductor Lasers and Their Applications

Semiconductor lasers are key components in many optical systems due to their advantages, including their small size, low cost, high efficiency, and low power consumption. It is well-known that semiconductor lasers under external perturbations, such as optical injection, optical feedback, or delayed coupling can exhibit a large variety of complex dynamical behaviors. Nowadays, cutting-edge engineering applications based on the complex dynamics of diode lasers are being conducted in areas, such as optical communications, optical signal processing, encoded communications, neuro-inspired ultra-fast optical computing devices, microwave signal generation, RADAR and LIDAR applications, biomedical imaging, and broadband spectroscopy. The prospects for these applications are even more exciting with the advent of photonic integrated circuits. This Special Issue focuses on theoretical and experimental advances in the nonlinear dynamics of semiconductor lasers subject to different types of external perturbations