Fuzzy Modeling and Synchronization of Chaotic Quantum Cellular Neural Networks Nano System via a Novel Fuzzy Model and Its Implementation on Electronic Circuits

Abstract

In this paper, a new fuzzy model is presented to simulate Quantum cellular neural networks nano system (called Quantum-CNN system). Through the new fuzzy model, the Quantum-CNN system is linearized to a simple form-linear coupling of two linear subsystems. Quantum-CNN system is a complicated nonlinear system. There are too more nonlinear terms in its dynamic equations, such as radical terms, square terms, sin and cos terms, etc. If the traditional T-S fuzzy model is used here, there would be 16 fuzzy rules and even 64 linear equations for modeling such a complex system. It is definitely an inefficient work. As a result, by using the new fuzzy model, the numbers of fuzzy rules can be reduced from 2(N) to 2 x N (where N is the number of nonlinear terms) and only two subsystems exist. Moreover, the LMI-based fuzzy synchronization of two fuzzy chaotic Q-CNN systems and its related theorem is proposed as well. Via using the new fuzzy model, only two feedback gains are needed in the fuzzy controllers. Finally, via using Taylor's expansion, the complicated nonlinear terms can be expanded to series form, and then the simplified Q-CNN system can be implemented on electronic circuits for secure communication. Simulation results in MATLAB and implementation of electronic circuits are given to show the effectiveness and feasibility of the new fuzzy model and the new approaches.