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Chaotic synchronization is a self-organizing phenomenon that occurs when two or more chaotic systems become synchronized. So far for multi-switching synchronization (MSS), only a homogeneous kind of switches have been discussed. This paper presents a generalized approach to MSS in which all possible heterogeneous combinations are presented. This generalization of MSS allows for greater flexibility and robustness in the MSS process. The switches are designed based on the order of the drive/response subsystems. The author also uses sliding mode control to achieve synchronization among various heterogeneous combinations during MSS. To demonstrate the effectiveness of the proposed approach, the author uses the Lorenz hyper chaotic system (LHCS) and the Chen hyper chaotic system (CHCS). The four different heterogeneous types of switches are designed and demonstrated for the chosen hyper chaotic systems. Mathematica is used for all numerical simulations. The results show that the proposed approach can achieve synchronization between two hyper chaotic systems with high accuracy. The author also shows that the proposed approach is robust to change in the parameters of the systems. This paper provides a new approach to chaotic synchronization that has potential applications in a variety of fields. The results presented in this paper are an important step towards the development of more robust and flexible synchronization schemes. [ABSTRACT FROM AUTHOR]

Complex composition engineering of mixed-cations perovskite (FA x MA 1-x PbI 3) has recently supported rapid progress in perovskite solar cells (PSCs). Nevertheless, it is insufficient to embed and accommodate formamidinium (FA) cation into the MAPbI 3 lattice structure v ia existing methods, leaving behind masses of FA or lead halide content and deteriorating photovoltaic performance. Herein, we present facile surface engineering v ia post-treated methodology, the surface of CH 3 NH 3 PbI 3 (MAPbI 3) films post-treated with formamidinium iodide (FAI) solution and that results get mixed-cation FA x MA 1-x PbI 3 perovskite films. The mixed-cation-based FA X MA 1-X PbI 3 perovskite with significant and large grain size, uniform and compact morphology, highly crystallization, and consequently reducing defect density of the perovskite films can be produced via the present method. It is observed that the film, post-treated with FAI-2, shows results in a very stable and highly crystalline lattice structure with attributes such as extended carrier lifetime, better electron transport, and decreased defect density. The optimized device demonstrates a promising power conversion efficiency (PCE) of 21.89%, and higher than that of the non-treated (19.08%) devices. Furthermore, the devices based on the novel FAI-post-treatment engineering exhibit significantly enhanced stability compared to non-treated devices. Therefore, this approach provides a novel methodology that offers a simple method for producing superior mixed perovskite films, potentially paving the way for the future exploitation of the boosted performance of perovskite solar cells. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we give the notion of M-η-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space, which is an extension of proximal mappings studied in [X.P. Ding, F.Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002) 369–383; K.R. Kazmi, M.I. Bhat, Convergence and stability of iterative algorithms of generalized set-valued variational-like inclusions in Banach spaces, Appl. Math. Comput. 113 (2005) 153–165; K.R. Kazmi, M.I. Bhat, N. Ahmad, An iterative algorithm based on M-proximal mappings for a system of generalized implicit variational inclusions in Banach spaces, J. Comput. Appl. Math. 233 (2009) 361–371]. We prove its existence and Lipschitz continuity in reflexive Banach space. Further, we consider a system of generalized implicit variational-like inclusions in Banach spaces and show its equivalence with a system of implicit equations using the concept of M-η-proximal mappings. Using this equivalence, we propose a new iterative algorithm for the system of generalized implicit variational-like inclusions. Furthermore, we prove the existence of solution of the system of generalized implicit variational-like inclusions and discuss the convergence and stability analysis of the iterative algorithm in the setting of uniformly smooth Banach spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of accretive mappings called generalized H(·,·)-accretive mappings in Banach spaces. We prove that the proximal-point mapping of the generalized H(·,·)-accretive mapping is single-valued and Lipschitz continuous. Further, we consider a system of generalized variational inclusions involving generalized H(·,·)-accretive mappings in real q-uniformly smooth Banach spaces. Using proximal-point mapping method, we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions. Furthermore, we discuss the convergence criteria of the iterative algorithm under some suitable conditions. Our results can be viewed as a refinement and improvement of some known results in the literature. [Copyright &y& Elsevier]

This article proves that the robust finite-time synchronization behavior can be achieved for the chaotic systems with different orders. Based on the Lyapunov stability theory and using the nonlinear feedback control, sufficient algebraic conditions are derived to compute the linear controller gains. These gains are then used to achieve the robust finite time increasing order and reduced order synchronization of the chaotic systems. This study also discusses the design of a controller that accomplishes the finite time synchronization of two chaotic systems of different dimensions under the effect of both unknown model uncertainties and external disturbances. Numerical simulation results are furnished to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this article, a novel robust nonlinear controller approach is focused to study theoretically, the reduced-order synchronization phenomena of two unrelated time-delayed chaotic systems under the determined and unknown parameters. It is assumed that the two systems are perturbed by the bounded unstructured uncertainties and unknown external disturbance. Based on the Lyapunov–Krasovskii functional theory, a robust nonlinear synchronization controller is focused and a suitable Lyapunov functional is constructed so that they establish the globally asymptotical stability of the closed-loop at the origin. Subsequently, suitable adaptive laws of unknown parameters are designed to identify the unknown parameters. Finally, the effectiveness of the proposed reduced-order synchronization approach is verified by numerical simulations. A brief comparison of the present study with prior works has been given. [ABSTRACT FROM AUTHOR]

Active control strategy is a powerful control technique in synchronizing chaotic/hyperchaotic systems. Until now, active control techniques have been employed to synchronize chaotic systems with the same orders. The present study overcomes the limitations of synchronization of chaotic systems of similar dimensions using active control. In this article, the authors investigate the synchronization problem for a drive-response chaotic system with different orders under the effect of both unknown model uncertainties and external disturbance. Based on the Lyapunov stability theory and Routh–Hurwitz criterion, a robust generalized active control approach is proposed and sufficient algebraic conditions are derived to compute a suitable linear controller gain matrix that guarantees the globally exponentially stable synchronization. Two examples are presented to illustrate the main results, namely reduced-order synchronization between the hyperchaotic Lu and the unified chaotic systems and the increased-order synchronization between the unified chaotic and the hyperchaotic Lu systems. There are three main contributions of the present study: (a) generalization of the active control for synchronization of a class of chaotic systems with different orders; (b) a recursive approach is proposed to compute a suitable linear controller gain matrix and (c) reduced (increased) order synchronization under the effect of both unknown model uncertainties and external disturbances. A comparative study has been done with our results and previously published work in terms of synchronization speed and quality. Future applications of the proposed reduced (increased) order synchronization approach are discussed. Finally, numerical simulations are given to verify the effectiveness of the proposed reduced (increased) order active synchronization approach. [ABSTRACT FROM AUTHOR]