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A simple three-dimensional (3D) autonomous chaotic system is extended to four-dimensions so as to generate richer nonlinear dynamics. The new system not only inherits the dynamical characteristics of its parental 3D system but also exhibits many new and complex dynamics, including assembled 1-scroll, 2-scroll and 4-scroll attractors, as well as hyperchaotic attractors, by simply tuning a single system parameter. Lyapunov exponents and bifurcation diagrams are obtained via numerical simulations to further justify the existences of chaos and hyperchaos. Finally, an electronic circuit is constructed to implement the system, with experimental and simulation results presented and compared for demonstration and verification. 相似文献
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为了实现不同类型混沌吸引子之间的复合,采用理论分析、数值仿真和电路仿真方法,通过设计合适的切换控制器实现了不同两涡卷混沌系统之间的复合、不同多涡卷混沌系统之间的复合、两涡卷混沌系统与两翅膀混沌系统之间的复合和多涡卷混沌系统与多翅膀混沌系统之间的复合.通过观察吸引子相图、最大Lyapunov指数和Poincaré截面,分析了复合系统的动力学行为.设计了复合多涡卷-多翅膀吸引子的模拟电路,并对其进行了电路仿真,得到的电路仿真结果与数值仿真结果相一致.这表明利用切换控制器实现不同类型混沌系统之间复合方法的正确性. 相似文献
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对于具有隐藏吸引子的混沌系统,既有文献大多只针对整数阶系统进行分析与控制研究.基于Sprott E系统,构建了仅有一个稳定平衡点的分数阶混沌系统,通过相位图、Poincare映射和功率谱等,分析了该系统的基本动力学特征.结果显示,该系统展现出了丰富而复杂的动力学特性,且通过随阶次变化的分岔图可知,系统在不同阶次下呈现出周期运动、倍周期运动和混沌运动等状态,这些动力学特征对于保密通信等实际工程领域有重要的研究价值.针对该具有隐藏吸引子的分数阶系统,应用分数阶系统有限时间稳定性理论设计控制器,对系统进行有限时间同步控制,并通过数值仿真验证了其有效性. 相似文献
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The object of this paper is to reveal the relation between dynamics of the fractional system and its dimension defined as a sum of the orders of all involved derivatives. We take the fractional Lorenz system as example and regard one or three of its orders as bifurcation parameters. In this framework, we compute the corresponding bifurcation diagrams via an optimal Poincaré section technique developed by us and find there exist two routes to chaos when its dimension increases from some values to 3. One is the process of cascaded period-doubling bifurcations and the other is a crisis (boundary crisis) which occurs in the evolution of chaotic transient behavior. We would like to point out that our investigation is the first to find out that a fractional differential equations (FDEs) system can evolve into chaos by the crisis. Furthermore, we observe rich dynamical phenomena in these processes, such as two-stage cascaded period-doubling bifurcations, chaotic transients, and the transition from coexistence of three attractors to mono-existence of a chaotic attractor. These are new and interesting findings for FDEs systems which, to our knowledge, have not been described before. 相似文献
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This paper proposes a new chaotic system and its fractional-order chaotic system. The necessary condition for the existence of chaotic attractors in this new fractional-order system is obtained. It finds that this new fractional-order system is chaotic for q 〉 0.783 if the system parameter m=6. The chaotic attractors for q=0.8, and q=0.9 are obtained. A circuit is designed to realize its fractional-order chaos system for q=0.9 by electronic workbench. 相似文献
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In this paper, the authors have studied the dynamics of a novel complex chaotic system with fractional order derivative and found the existence of chaos. The novel complex system is simulated for integer as well as fractional orders which shows some unusual phenomena. The main contribution of this effort is an implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf’s algorithm. The conditions for chaos control based on the fractional Routh–Hurwitz stability conditions and feedback control are given. Also synchronization between a fractional order novel chaotic system and a controlled fractional order novel system using the modified adaptive projective synchronization method for different scaling matrices has been obtained. Numerical simulation results are carried out using the Adams–Bashforth–Moulton method. 相似文献
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This paper studies the control of a new chaotic system which can
generate 4-scroll attractors. Based on the properties of a passive
system, it derives the essential conditions under which this new
chaotic system could be equivalent to a passive system and globally
asymptotically stabilize at a zero equilibrium point via smooth
state feedback. Simulation results and circuit experiment show that
the proposed chaos control method is effective. 相似文献
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The hybrid projective synchronization of different dimensional fractional order chaotic systems is investigated in this paper. It is shown that the slave system can be synchronized with the projection of the master system generated through state transformation. Based on the stability theorem of linear fractional order systems, a suitable controller for achieving the synchronization is given. The hybrid projective synchronization between the fractional order chaotic system and hyperchaotic system is successfully achieved in both reduced order and increased order. The corresponding numerical results verify the effectiveness of the proposed method. 相似文献
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In this Letter, a kind of novel model, called the generalized Takagi-Sugeno (T-S) fuzzy model, is first developed by extending the conventional T-S fuzzy model. Then, a simple but efficient method to control fractional order chaotic systems is proposed using the generalized T-S fuzzy model and adaptive adjustment mechanism (AAM). Sufficient conditions are derived to guarantee chaos control from the stability criterion of linear fractional order systems. The proposed approach offers a systematic design procedure for stabilizing a large class of fractional order chaotic systems from the literature about chaos research. The effectiveness of the approach is tested on fractional order Rössler system and fractional order Lorenz system. 相似文献
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In this paper, two kinds of novel non-ideal voltage-controlled multi-piecewise cubic nonlinearity memristors and their mathematical models are presented. By adding the memristor to the circuit of a three-dimensional jerk system, a novel memristive multiscroll hyperchaotic jerk system is established without introducing any other ordinary nonlinear functions, from which \(2N+2\)-scroll and \(2M+1\)-scroll hyperchaotic attractors are achieved. It is exciting to note that this new memristive system can produce the extreme multistability phenomenon of coexisting infinitely multiple attractors. Furthermore, the dynamical behaviours of the proposed system are analysed by phase portraits, equilibrium points, Lyapunov exponents and bifurcation diagrams. The results indicate that the system exhibits hyperchaotic, chaotic and periodic dynamics. Especially, the phenomenon of transient chaos can also be found in this memristive multiscroll system. Additionally, the MULTISIM circuit simulations and the hardware experimental results are performed to verify numerical simulations. 相似文献
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Mohammad Pourmahmood Aghababa 《中国物理 B》2012,21(10):100505-100505
The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electromechanical resonator system(FOMEMRS).Using the maximal Lyapunov exponent criterion,we show that the FOMEMRS exhibits chaos.Strange attractors of the system are plotted to validate its chaotic behavior.Afterward,a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time.Using the latest version of the fractional Lyapunov theory,the finite time stability and robustness of the proposed scheme are proved.Finally,we present some computer simulations to illustrate the usefulness and applicability of the proposed method. 相似文献
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Mayank Srivastava Saurabh K. Agrawal Subir Das 《Central European Journal of Physics》2013,11(10):1504-1513
The article aims to study the reduced-order anti-synchronization between projections of fractional order hyperchaotic and chaotic systems using active control method. The technique is successfully applied for the pair of systems viz., fractional order hyperchaotic Lorenz system and fractional order chaotic Genesio-Tesi system. The sufficient conditions for achieving anti-synchronization between these two systems are derived via the Laplace transformation theory. The fractional derivative is described in Caputo sense. Applying the fractional calculus theory and computer simulation technique, it is found that hyperchaos and chaos exists in the fractional order Lorenz system and fractional order Genesio-Tesi system with order less than 4 and 3 respectively. The lowest fractional orders of hyperchaotic Lorenz system and chaotic Genesio-Tesi system are 3.92 and 2.79 respectively. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method, shows that the method is reliable and effective for reduced order anti-synchronization. 相似文献
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Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization
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Based on the stability theory of the fractional order system,the dynamic behaviours of a new fractional order system are investigated theoretically.The lowest order we found to have chaos in the new three-dimensional system is 2.46,and the period routes to chaos in the new fractional order system are also found.The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent.Furthermore,a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system,and its validity is proved by Laplace transformation theory. 相似文献
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A novel 3D fractional-order chaotic system is proposed in this paper. And the system equations consist of nine terms including four nonlinearities. It's interesting to see that this new fractional-order chaotic system can generate one-wing, two-wing, three-wing and four-wing attractors by merely varying a single parameter. Moreover, various coexisting attractors with respect to same system parameters and different initial values and the phenomenon of transient chaos are observed in this new system. The complex dynamical properties of the presented fractional-order systems are investigated by means of theoretical analysis and numerical simulations including phase portraits, equilibrium stability, bifurcation diagram and Lyapunov exponents, chaos diagram, and so on. Furthermore, the corresponding implementation circuit is designed. The Multisim simulations and the hardware experimental results are well in accordance with numerical simulations of the same system on the Matlab platform, which verifies the correctness and feasibility of this new fractional-order chaotic system. 相似文献
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利用Silnikov定理,讨论了具有自动频率跟踪功能电磁振动机械系统的混沌特性.借助卡尔达诺公式和微分方程组级数解分别讨论了该系统的特征值问题和同宿轨道的存在性,进而比较严密地证明了该系统Silnikov型Smale混沌的存在性,并给出发生Silnikov型Smale混沌所需条件.利用数值模拟得到该类机电耦合系统的相轨迹图、Lyaponov指数谱和Lyaponov维数,进一步验证了该非线性系统存在奇怪吸引子.
关键词:
混沌系统
Lyapunov指数
Silnikov定理
耦合 相似文献
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Projective synchronization of a complex network with different fractional order chaos nodes
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Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lü system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme. 相似文献