Study On Modeling, Control And Applications Of Several Kinds Of Multi-scroll And Multi-wing Chaotic Systems

Modeling, control and applications of several kinds of multi-scroll and multi-wing chaotic systems are studied in this dissertation, which are current research focuses in the field of chaos at home and abroad. The modelling of chaotic systems includes the design of several typical multi-scroll chaotic and multi-wing chaotic systems. The control of chaotic systems is mainly to design both grid multi-scroll chaotic attractors and compound chaotic attractors by switching control. Based on modeling, analysis and control of chaos, some applications of chaos are further investigated including circuits design for multi-scroll and multi-wing chaotic systems, speech chaotic secure communication and digital image encryption. The three types of research topics of this dissertation are introduced in detail as follows.The first part is "modelling of chaotic systems". Several typical multi-scroll chaotic systems, grid multi-scroll chaotic systems, multi-wing chaotic systems, grid multi-wing hyperchaotic systems are proposed. The following four aspects are developed.(1) A multi-scroll chaotic system is proposed. It is confirmed that different types of multi-scroll chaotic attractors are available by constructing triangular wave, sawtooth wave, hysteresis series, sinusoidal function and 2n multiple angle of cosinusoidal function.(2) An approach for generating two types of grid multi-scroll chaotic attractors from canonical Chua's circuit is reported. Different from the techniques reported by existing literatures for generating multi-scroll chaotic attractors by constructing only the same type of non-linear function, the presented approach can construct both hysteresis series and step series in the same Chua's circuit, and extend the saddle-focus equilibrium points with index-2 in phase space by combining the both series in different ways, which makes it possible to create two kinds of grid multi-scroll chaotic attractors.(3) Two integer-order and one fractional-order multi-wing chaotic attractors are designed. Both piecewise-linear Chen system and a newly three-dimensional quadratic double-wing chaotic are invariant under the transformation of (x,y.z)→(-x.-y,z), therefore, multi-wing chaotic attractors from them can be generated by constructing a duality-symmetric multi-segment quadratic function. A systematic design and circuit implementation for creating fractional-order multi-wing chaotic attractors are further investigated. Based on a fractional-order linear differential system, by introducing the nonlinear state feedback controller, various fractional-order 2n(n=1,2···)-wing chaotic attractors can be generated.(4) Some approaches for constructing various complex grid multi-wing 4-D hyperchaotic Lu systems are reported. By shift transformation, mirror symmetry conversion and rotation transformation, three classes of complex grid n×m-wing hyperchaotic systems are respectively obtained. One characteristic of the proposed approaches lies in their generality, which is also suitable for constructing 4-D grid multi-wing hyperchaotic Lorenz-like systems such as multi-wing hyper-Lorenz and multi-wing hyper-Chen.The second part is "switching control of chaotic systems". Via switching control, both grid multi-scroll chaotic attractors and compound chaotic attractors can be created. To be specific, two tasks are investigated as follows.(1) A method is developed for generating grid multi-scroll chaotic attractors using switching piecewise linear controller. First, a third-order linear system is designed to ensure that its unique equilibrium point belongs to a saddle-focus type with index 2 and the corresponding eigenvalues satisfy Shilnikov conditions. Then, by step, transition and hysteresis switching control strategies, the original third-order linear system can be divided into several different linear subspace and grid multi-scroll chaotic attractors can be generated, which is chaotic in the sense of Smale horseshoe from Shilnikov theorem.(2) A new autonomous-system-based approach for creating compound chaotic attractors via switching control is reported. First, several generalized Lorenz systems are selected, and the state variable scale transformation is made for these selected systems to ensure all attractors with the approximately size. Coordinate transformation in(?)axis direction is also used so that there exists the common connected domain for every two adjacent chaotic attractors in the same phase space. Then, by switching control, the various compound chaotic attractors can be generated.The third part is "application research", including both circuit design and secure communication of chaotic systems. On one hand, module-based circuits for multi-scroll and multi-wing chaotic systems are designed and implemented, which are created from chapter 2 to chapter 7. On the other hand, speech wire, speech wireless chaotic digital communication and an image encryption scheme based on n (n≥8) dimension (n-D) generalized hyper-chaotic cat map are investigated, which are described in detail as follows.(1) A scheme for hyperchaotic secure communication based on ring coupled RC oscillators is proposed. The presented scheme uses RC oscillator-based hyperchaotic signal generators and nonlinear ring couplers, from which information encryption and decryption can be realized. Furthermore, this approach is designed and implemented by digital signal processor (DSP).(2) A system design and hardware realization of speech wireless chaotic digital communication via digital signal processor (DSP) is proposed. Multi-scroll generalized Jerk is used for speech data encryption and decryption. Base on the DSP technical platform with TMS320VC5509APGE chip, by utilizing wireless transmitter and receiver nRF2401, speech wireless chaotic digital communication is successfully implemented. The results of technical design and hardware realization are also given, which confirms the feasibility of the scheme.(3) An image encryption scheme is investigated based on n (n≥8) dimension (n-D) generalized hyper-chaotic cat map. Based on 2-D and 3-D cat map, the n-D generalized hyper-chaotic cat map is constructed, which is applied to image encryption. Here, the possible sorting numbers of transformation sub-matrix T(?) multiplication are used as encrypted keys, compared with existing low-dimension (n≤4) cat map, high-dimension (n≥8) generalized hyper-chaotic cat map exists bigger encryption key spaces and two positive Lyapunov exponents. Both theoretical analysis and numerical experiment results have confirmed the feasibility of the proposed method.This work was supported by the National Natural Science Foundation of China under Grants 60871025, the Natural Science Foundation of Guangdong Province under Grants 8151009001000060 and 8351009001000002, the Science and Technology Program of Guangdong Province under Grant 2009B010800037, and subproject of the third important subject construction of Guandong "211 Projects" (Guangdong Development and Reform Commission [431]).