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Abstract In this paper, based on linear matrix inequality technique, a simple controller and a compensatory controller are designed. It can track arbitrary fixed points and any periodic orbits. In addition, a synchronization control method via Chebyshev neural network with external disturbances is proposed. An adaptive controller is given. The Chebyshev neural network is used to approximate the uncertain nonlinear function and the adaptive law is used to adjust the corresponding parameters in the system. Taking a 4D memristive chaotic system as examples, the results are in consistent with the simulations. From a framework and control theoretical point of view, the proposed synchronization approach via compensation controller and Chebyshev neural network is firstly presented. From an application point of view, the proposed scheme can simplify the complexity of controller design. It is promising in many applications for mem-systems as secure communications and neural networks.

The goal of this article is to obtain soliton cluster solutions of (2 + 1)-dimensional nonlinear variable coefficient Schrödinger equations through computerized symbolic computation. By applying the self-similarity method, one soliton solution is constructed for the NLS equations with variable coefficient, which provide a model of the propagation of the soliton waves. Consequently, the solitonary cluster solution is achieved in different structures. Additionally, the propagation of the obtaining solitonary cluster solutions is analyzed and discussed. The results are useful to explain the soliton phenomena in nonlinear optics.

By using linear entropy, a discrete quantum logistic chaotic map is introduced and the dynamical evolution of the quantum radiation field interacting with the matter is studied by changing the independent parameters. Its typical effect is the chaotic property of the quantum optics and a quantum classical correspondence is obtained, and the chaos and the regular structure of phase space can be better revealed by using the coherence dynamics of phase space. In addition, an approach for fast adaptive synchronization of the discrete quantum maps is proposed. Results validate the effectiveness of the proposed scheme.

A (1 + 1)-dimensional Korteweg-de Vries (KdV) equation is studied. Using the extended Tanh-function method, the analytical soliton solutions are obtained by symbolic calculation, and the localized coherent structures containing the compacton, the peakon, periodic multi-solitons and fractal soliton structures are constructed. Through the analysis of various images, the properties of soliton solutions excited by different local structures are discussed and the fractal structure of soliton solutions are further discussed.

Abstract One‐step deposition approaches have been widely applied and developed in the fabrication of quasi‐2D perovskites. However, the regulation of quantum wells (QWs) and crystalline orientation is difficult and complicated when using this methodology. Sequential deposition is another widespread synthetic approach for preparing perovskite films and perovskite dimension engineering. In this article, δ‐CsPbI3 intermediate phase assisted sequential (IPAS) deposition is successfully carried out to fabricate MA‐free quasi‐2D ACI perovskites. The amount of the δ‐CsPbI3 intermediate phase in the PbI2 layer and the concentration of GAI molecule in the IPA solution both play important roles in the production of MA‐free quasi‐2D ACI perovskite films. The n value of the MA‐free quasi‐2D ACI perovskites can be adjusted, which affects the photovoltaic performance and device stability. Compared with one‐step deposition, the MA‐free quasi‐2D ACI perovskites prepared via IPAS deposition have opposite reverse‐graded QW distribution and improved vertical orientation, leading to a remarkable PEC of up to 18.86% and allowing the preparation of unpackaged devices with prominent working stability (80%, ~400 h). The underlying mechanism and crystallization pathway of IPAS deposition confirm that sequential deposition has unique superiority in regulating the QW distribution and crystalline orientation of quasi‐2D perovskites.

A novel hyperchaotic system with only one equilibrium point is proposed by introducing an additional state feedback. The dynamic behaviors of this system are investigated by means of the Lyapunov exponent, Poincaré map, and bifurcation diagrams, i.e., this new hyperchaotic system possesses two positive Lyapunov exponents within a large range. Interestingly, the chaotic attractor of the system is special with two slow and fast attractors, that is, the system is a combination of slow and fast parts. The bound estimation of this system is also investigated. In addition, the image cryptology method is performed. In the image encryption part, an algorithm is suggested to provide confusion and diffusion operations on the image. The results show that, by employing the hyperchaotic system, the original image information can be completely hidden after being encrypted and can be decrypted efficiently.

The Hirota bilinear method is applied to construct the new dynamics of complex N-soliton solutions for a nonlocal breaking equation. By using the auxiliary traveling wave function, the different-order soliton solutions, bifurcation solutions and lump solutions of the model are obtained. The complex variable for Hirota bilinear form of this breaking equation is derived firstly via logarithmic variable transform. The physical phenomena and soliton propagation behavior of these solutions are explored, and the obtained results verify the proposed soliton solutions.