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This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display different attractors with two unstable equilibrium points and four unstable equilibrium points respectively. Dynamical properties of this system are then studied. Furthermore, by applying the undetermined coefficient method, heteroclinic orbit of (S)hil'nikov's type in this system is found and the convergence of the series expansions of this heteroclinic orbit are proved in this article. The (S)hil'nikov's theorem guarantees that this system has Smale horseshoes and the horseshoe chaos. 相似文献
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In this paper, we discuss a type of chaotic system with delays. We study the equilibrium points and the existence of heteroclinic orbit of the system. Heteroclinic orbit existence theorem is proposed and proved by applying the undetermined coefficient method, which shows the complex dynamical properties of this system. 相似文献
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Generation of countless embedded trumpet-shaped chaotic attractors in two opposite directions from a new three-dimensional system with no equilibrium point 下载免费PDF全文
A new three-dimensional(3D) continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directions are generated from the system as time goes on. The basic dynamical behaviors of the strange chaotic system are investigated. Another more complex 3D system with the same capability of generating countless embedded trumpet-shaped chaotic attractors is also put forward. 相似文献
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运用Silnikov定理构建一个具有共存吸引子且个数可调的混沌系统.首先在经典混沌系统基础上构建一个结构简单的混沌系统,分析系统的动力学特性,验证系统马蹄意义下的混沌特性.在此基础上,将多零点分段函数引入该系统,以扩展系统平衡点的方式来增加系统的不变集,进而建立具有共存吸引子个数可调的混沌系统,由于共存吸引子的复杂性,... 相似文献
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为了产生复杂的混沌吸引子,构造了一个新的三维二次自治混沌系统.该系统含有三个参数,每一个方程含有一个非线性乘积项.利用理论推导、数值仿真、Lyapunov指数谱和分岔图对系统的基本动力学特性进行了分析.结果表明,该系统具有五个平衡点,因而与Lorenz,Rsslor,Chen、Lü等混沌系统是非拓扑等价的;当其参数满足一定条件时,系统是混沌的.与Lorenz等混沌系统相比,该系统具有更大的正Lyapunov指数,能够产生复杂的混沌吸引子和一些有趣的动力学行为.最后,设计了实现该系统的混沌电路,电路实验结
关键词:
三维二次自治系统
混沌
混沌吸引子
电路实现 相似文献
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Jesus M. Munoz-Pacheco Christos Volos Fernando E. Serrano Sajad Jafari Jacques Kengne Karthikeyan Rajagopal 《Entropy (Basel, Switzerland)》2021,23(7)
In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system. 相似文献
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提出了一个新的简单的双曲型三维自治混沌系统,该三维混沌系统只含有五项, 并且其非线性特征主要依赖于一个非线性二次双曲正弦项和一个非线性二次交叉项. 较已有的三维混沌系统而言, 不仅系统的项要少一些, 而且在参数变化时, 呈现混沌的参数范围也很大. 对系统的一些基本动力学特性进行了数值模拟和理论分析. 同时, 还研究了具有完全不确定参数的该五项双曲型混沌系统的投影同步. 基于Lyapunov指数稳定性理论和Barbalat引理, 设计了一个新的具有参数自适应律的自适应同步控制器, 利用该控制器分别实现了两个结构相同和相异混沌系统的渐进性和全局性投影同步. 数值模拟验证了该方法的有效性和可行性. 相似文献
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Traditional machine-learning methods are inefficient in capturing chaos in nonlinear dynamical systems, especially when the time difference between consecutive steps is so large that the extracted time series looks apparently random. Here, we introduce a new long-short-term-memory (LSTM)-based recurrent architecture by tensorizing the cell-state-to-state propagation therein, maintaining the long-term memory feature of LSTM, while simultaneously enhancing the learning of short-term nonlinear complexity. We stress that the global minima of training can be most efficiently reached by our tensor structure where all nonlinear terms, up to some polynomial order, are treated explicitly and weighted equally. The efficiency and generality of our architecture are systematically investigated and tested through theoretical analysis and experimental examinations. In our design, we have explicitly used two different many-body entanglement structures—matrix product states (MPS) and the multiscale entanglement renormalization ansatz (MERA)—as physics-inspired tensor decomposition techniques, from which we find that MERA generally performs better than MPS, hence conjecturing that the learnability of chaos is determined not only by the number of free parameters but also the tensor complexity—recognized as how entanglement entropy scales with varying matricization of the tensor. 相似文献
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研究了异结构混沌系统之间的同步控制问题.采用非线性反馈控制方法实现了3D混沌系统和单模激光Lorenz混沌系统之间的混沌同步.根据系统的稳定性理论,得到了非线性反馈控制器的结构和反馈控制增益的取值范围.仿真模拟的结果表明:目标系统和响应系统达到完全同步,两系统状态变量随时间的演化轨迹完全一致,并且误差变量经过短暂的时间序列以后始终平稳地趋于零.仿真模拟的结果证明了这种方法的有效性. 相似文献
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ZHOU Yun ZHU Shi-Qun WU Liang 《理论物理通讯》2005,44(6):1076-1080
In a coupled laser system, the dynamics of the receiving laser is investigated when two separate transmitting lasers are injected into the receiving laser with different coupling strengths. It is shown that the phenomenon of preference of chaotic synchronization appears under appropriate coupling conditions. The receiving laser will entrain the pulses of either one or both transmitting lasers when the coupling is strong while it keeps its own dynamics when the coupling is weak. 相似文献
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ZHOU Yun ZHU Shi-Qun WU Liang 《理论物理通讯》2005,44(12)
In a coupled laser system, the dynamics of the receiving laser is investigated when two separate transmitting lasers are injected into the receiving laser with different coupling strengths. It is shown that the phenomenon of preference of chaotic synchronization appears under appropriate coupling conditions. The receiving laser will entrain the pulses of either one or both transmitting lasers when the coupling is strong while it keeps its own dynamics when the coupling is weak. 相似文献
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In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos. 相似文献
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In response to the problems of high complexity and the large amount of operations of existing color image encryption algorithms, a low-complexity, low-operation color image encryption algorithm based on a combination of bit-plane and chaotic systems is proposed that is interrelated with plaintext information. Firstly, three channels of an RGB image are extracted, and the gray value of each pixel channel can be expressed by an eight-bit binary number. The higher- and lower-four bits of the binary gray value of each pixel are exchanged, and the position of each four-bit binary number is scrambled by a logistic chaotic sequence, and all the four-bit binary numbers are converted into hexadecimal numbers to reduce the computational complexity. Next, the position of the transformed image is scrambled by a logistic chaotic sequence. Then, the Chen chaos sequence is used to permute the gray pixel values of the permuted image. Finally, the gray value of the encrypted image is converted into a decimal number to form a single-channel encrypted image, and the three-channel encrypted image is synthesized into an encrypted color image. Through MATLAB simulation experiments, a security analysis of encryption effects in terms of a histogram, correlation, a differential attack, and information entropy is performed. The results show that the algorithm has a better encryption effect and is resistant to differential attacks. 相似文献
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Giuseppe Grassi 《中国物理 B》2008,17(9):3247-3251
This paper presents the problem of generating four-wing (eight-wing) chaotic attractors. The adopted method consists in suitably coupling two (three) identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings (eight wings) of these novel attractors axe located around the four (eight) equilibria with two (three) pairs of unstable complex-conjugate eigenvalues. 相似文献
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CHEN Yong YAN Zhen-Ya 《理论物理通讯》2008,49(4):951-954
In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods (the linear, speed, doubly-periodic function controller) to suppress the chaos to unstable equilibrium. As a result, some controllers are obtained. Moreover, numerical simulations are used to verify the effectiveness of the obtained controllers. 相似文献