Marius-F. Danca, Nikolay Kuznetsov
In this letter we unveil the existence of transient hidden coexisting chaotic attractors, in a simplified Hopfield neural network with three neurons.
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Approximation and decomposition of attractors of a Hopfield neural network system
本文将参数切换（PS）算法用于Hopfield神经网络（HNN）系统吸引子的数值逼近，证明其吸引子可表示为其他吸引子的凸组合，且HNN系统可改写为适配PS算法的形式，为混沌调控提供了新的可能路径。
Persistence and Doubling of Chaotic Attractors in Coupled 3-Cell Hopfield Neural Networks
本研究针对单向耦合3细胞Hopfield神经网络，发现并验证了混沌持续性与混沌吸引子倍增两种新现象，严格证明了相关特性，还展示了多重重叠混沌吸引子并讨论超混沌形成。
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The Parameter Switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustra…
In [1], it is shown that the Rabinovich-Fabrikant (RF) system admits self-excited and hidden chaotic attractors. In this paper, we further show that the RF system also admits a pair of symmetric transient hidden chaotic attractors. We reveal more extremely rich dynamics of this system, such as a new kind of "virtual saddles".
Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor
在本文中，我们证明，首先在我们已知的文献中，可以在连续耗散混沌系统中构造势函数，并可以用来揭示其动力学性质。为了达到这一目的，提出了一个Lorenz类系统，并严格证明了混沌的例子分析。我们明确地构造了一个沿系统动力学单调递减的势函数，揭示了混沌奇异吸引子的结构。势函数可以有不同的构造形式。我们还对动力系统进行了分解，解释了混沌吸引子和奇异吸引子的不同起源。因此，在现有的分解框架下，混沌非奇异吸引子和非混沌奇异吸引子同时存在的原因得到了清楚的讨论。
Stability enhanced by transient attractors in a memristive chaotic map
本文通过将离散忆阻器模型与混沌映射耦合，发现忆阻器的引入显著扩大混沌吸引子的吸引域，从而增强其稳定性，该效应源于忆阻器的记忆与开关特性。
Chaotic mechanism description by an elementary mixer for the template of an attractor
本文提出用基本混合器及其链接矩阵唯一描述混沌吸引子的模板与机制，并通过混合器拼接建立按规模分类混沌机制的统一框架。
Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized to show the presence of unpredictability.
Chaotic dynamics of the Hunt model, an artificially constructed flow system with a hyperbolic attractor
研究了Hunt模型中Plykin型双曲奇异吸引子的混沌行为。有吸引子的画像，图的实现由系统产生的混沌信号，插图的敏感依赖于初始条件的吸引子上的轨迹。定量特征的吸引子估计，包括李雅普诺夫指数和吸引子维数。讨论了吸引子上的符号动力学，找出并分析了吸引子上的不稳定周期轨道。
Analysis of Two Time Scale Property of Singularly Perturbed System on Chaotic Attractor
本文考虑了混沌可以作为分析非线性系统的有用工具的思想，首次从混沌吸引子的角度分析了奇异摄动系统的双时标性质。本文提出的一般思想是：混沌系统在相空间中具有有序的奇异吸引子，这种有序性与其它类型的混沌系统相一致，可用于分析。在这里，奇异摄动系统下标混沌系统。讨论了系统的双时标特性。利用混沌吸引子的有序性分析了相平面上的双时标行为。
Coexistence of exponentially many chaotic spin-glass attractors
研究了一个具有时滞作用的混沌网络，其规模为$N$，类似于一个伪逆联想记忆神经网络。对于一个负载$α=P/N<1$，其中$P$代表存储模式的数量，混沌网络的功能是一个2 P吸引子的联想记忆，其宏观吸引盆随着$α$而减小.在有限的$α$，存在一个混沌自旋玻璃相，其中不同的混沌吸引子的数量与$N$呈指数关系。每个吸引子的特征在于混沌行为和每个$N$混沌单元的冻结或相对于$P$模式的冻结的共存。结果支持由伯努利映射单元和Mackey-Glass时间延迟微分方程组成的网络的大规模模拟。
Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations
数值研究了一类具有突变过程的复制子方程。在没有任何突变的情况下，复制子动力学的两个特征是已知的：优势期的指数发散和吸引子的层次排序。突变引入了一些新的方面：结构稳定吸引子的出现，以及混沌巡游行为。此外，在突变率-> +0区域内，还发现了中性吸引子的存在.
Divergence Measure Between Chaotic Attractors
我们提出了一种度量概率分布的发散度的方法来量化两个混沌吸引子的相异性。这个度量是用广义熵来定义的。我们说明了我们的程序，考虑加性噪声的影响，在著名的Hénon吸引子。对两个参数值略有不同的Hénon吸引子的比较表明，发散具有复杂的标度结构。最后，我们展示了我们的方法如何允许检测时间序列中的非平稳事件。
Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons
研究了两个耦合的分段线性一维单稳映射的动力学。单个映射与FitzHugh-Nagumo神经元模型的庞加莱部分相关联。结果表明，扩散耦合导致混沌吸引子的出现。该吸引子存在于以鞍不动点和鞍周期点的流形为界的相空间的不变区域中。从混沌吸引子的振荡有一个尖峰脉冲的形状与反相同步尖峰。
Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems
本文利用全局耦合映射研究了高维动力系统中Milnor吸引子的优势。从数值模拟中，Milnor吸引子的这种流行度的自由度的阈值数被建议为$5 \sim 10$，这也是估计从盆地边界的组合爆炸的参数。从Milnor吸引子的观点重新讨论了混沌巡游。讨论了与神经网络的相关性。
Gibbs attractor: a chaotic nearly Hamiltonian system, driven by external harmonic force
一个混沌自治Hamilton系统，在小阻尼和小外力的扰动下，谐地依赖于时间，可以获得一个性质类似于正则分布的奇异吸引子--Gibbs吸引子.在这样的系统中的能量的演化可以被描述为能量扩散。对两自由度非线性Pullen-Edmonds振子，用解析和数值方法研究了Gibbs吸引子的性质及其对扰动参数的依赖性。
Inherent Frequency and Spatial Decomposition of the Lorenz Chaotic Attractor
这封信提出了一种新的方法来研究三维混沌的空间和频率域同时进行。通过将Lorenz混沌吸引子空间分解为两个谱峰的涡卷和一个谱宽的一维离散过零序列，发现Lorenz混沌吸引子具有由三个系统参数唯一确定的固有频率.这一结果意味着，混沌的洛伦兹吸引子主要表现在轨迹从一个涡卷到另一个涡卷，而不是在两个涡卷。这也适用于其他一些双涡卷类Lorenz混沌吸引子，如蔡氏吸引子。文中还讨论了固有频率和空间分解的一些可能的应用。
Optimum PID Control of Multi-wing Attractors in A Family of Lorenz-like Chaotic Systems
多翼混沌吸引子是一种高度复杂的非线性动力系统，具有较多的指数2平衡点。由于多个平衡点的存在，这些多翼混沌系统的状态时间序列的随机性高于传统的双翼混沌吸引子。提出了一种基于实数编码遗传算法（GA）的全局优化框架，设计了最优PID控制器，并对Lu、Rucklidge和Sprott-1三个多翼类Lorenz混沌系统的状态轨迹进行了控制。
Peeling Bifurcations of Toroidal Chaotic Attractors
具有环形拓扑的混沌吸引子（van der Pol吸引子）具有对称性，表现出不熟悉的现象。我们调查双覆盖的环形吸引子，讨论其形态的变化下相关剥离分叉，描述其拓扑结构和所经历的变化作为一个对称轴穿过原始吸引子，并指出如何符号名称的轨迹在原来的升降机在封面上。覆盖轨道描述使用一个强大的合成揉捏理论与改进的圆映射。这些方法适用于一个简单的版本的范德波尔振荡器。
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unsta…
We discuss two mechanical systems with hyperbolic chaotic attractors of Smale - Williams type. Both models are based on Froude pendulums. The first system is composed of two coupled Froude pendulums with alternating periodic braking. The second system is Froude pendulum with time-delayed feedback and periodic braking. We demonstrate by means of numerical simulations that proposed models have chaotic attractors of Smale - Williams type. We specify regions of parameter values at which the dynamics corresponds to Smale - Williams solenoid. We check numerically hyperbolicity of the attractors.
Parry measure and the topological entropy of chaotic repellers embedded within chaotic attractors
本文研究了混沌吸引子中不访问相空间中某个小的禁带区域的点所形成的混沌排斥子的拓扑熵。洞是相空间中的一组点，这些点具有序列$α=(α_0α_1...α_{l-1})$作为其行程中的第一个$l$字母。我们指出，对于$α$的大多数选择，吸引子和嵌入排斥子的拓扑熵之差近似等于对应于$α$的Parry测度，即$μ_P(α)$ .当空穴包含短周期轨道的一点时，熵差明显小于$μ_P(α)$。这种差异是描述的公式，其中涉及的短周期轨道的长度，帕里措施$μ_P(α)$，和两个混沌集的拓扑熵。
In this paper, based on the classic Chua's circuit, a charge-controlled memristor is introduced to design a novel four-dimensional chaotic system. The complex dynamics of the novel chaotic system such as equilibrium points, stability, dissipation, bifurcation diagrams, Lyapunov exponent spectra and phase portraits are investigated. By varying the initial conditions of the system, it is found from numerical simulations that the system shows some dynamics of great interests including double-wings chaotic attractors, coexisting periodic-chaotic bubbles, asymmetric and symmetric coexisting attrato…
The topology of a chaotic attractor in the Kuramoto-Sivashinsky equation
研究混沌发生时的Kuramoto-Sivashinsky PDE，利用本征正交分解和自编码器两种降维技术将混沌吸引子映射至三维，通过分析UPOs的交叉数构建等价的拓扑模板，证实了降维的稳健性与拓扑表征的准确性。
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labelling. Addressing these problems correspond to the development of a dynamical taxonomy, exhibiting the key properties discriminating the variety of chaotic behaviors discussed in the abundant literature. Starting from the hierarchy of chaos initially proposed by one of us, we systematized the description of chaotic regimes observed in three- and four-dime…
Driving--induced bistability in coupled chaotic attractors
我们研究的影响，对称性-保持和打破相互作用的驱动-响应系统的响应具有不变的对称性，在没有驱动器。在广义同步开始之后，我们发现可以有不止一个稳定的吸引子。数值，以及分析结果建立在这种共存的吸引相同步的存在。这些结果对外部噪声是鲁棒的。
Chaotic itinerancy and power-law residence time distribution in stochastic dynamical system
为了研究有序状态间的混沌巡游运动，基于混沌巡游机制，提出了一种随机模型。该模型由半直线上的随机游动和带有转移概率矩阵的马尔可夫链组成。为了研究模型中吸引子废墟的稳定性，我们分析了轨道在吸引子废墟处的停留时间分布。我们表明，所有吸引子废墟平均的停留时间分布是由（截断）幂律分布的叠加，如果一个盆地的吸引力为每个吸引子废墟有零措施。为了证实这一结果，我们对表现混沌巡游的模型进行了计算机模拟。讨论了当吸引子废墟之间的转移概率可用马尔可夫链表示时，耦合的Milnor吸引子系统不发生混沌巡游。
Parametric characterisation of a chaotic attractor using two scale Cantor measure
一个混沌吸引子的特征通常是它的多重分形谱，它给出了它的复杂性的几何度量。在这里，我们提出了一个使用最小的一组独立的参数，这是唯一确定的基本过程中产生的吸引子的特性。该方法将一个混沌吸引子的f（alpha）谱映射到一个一般的双尺度Cantor测度的f（alpha）谱上。我们表明，映射可以做大量的混沌系统。为了实现这一过程，我们还提出了一个推广的标准方程的两个尺度康托集在一维到更高的维度。另一个有趣的结果，我们已经得到了理论和数值是，f（alpha）的特性只给信息高达两个尺度，即使当底层的过程中产生的多重分形涉及两个以上的尺度。
Minimal cover of high-dimensional chaotic attractors by embedded recurrent patterns
提出一种通过嵌入不稳定递归模式构建高维混沌吸引子极小覆盖的通用方法，证明在低维子空间定义邻近度也能忠实构建极小覆盖，可用于简化描述吸引子结构与动力学。
Limit Distribution of Averages over Unstable Periodic Orbits Forming Chaotic Attractor
我们解决了一个单一的长不稳定的周期轨道的混沌吸引子，它是嵌入在属性的代表性问题。Y. Saiki和M. Yamada [Phys.Rev.E79，015201（R）（2009）]最近提出了这样的假设，即在具有给定圈数N的不稳定周期轨道上存在平均值的极限分布，对于无限长的轨道，它不是Dirac δ函数。在本文中，我们证明了极限分布实际上是一个δ函数和标准偏差衰减为1/sqrt（N）足够大的N。
Chaotic attractors are solutions of deterministic processes, of which the topology can be described by templates. We consider templates of chaotic attractors bounded by a genus-1 torus described by a linking matrix. This article introduces a novel and unique tool to validate a linking matrix, to optimize the compactness of the corresponding template and to draw this template. The article provides a detailed description of the different validation steps and the extraction of an order of crossings from the linking matrix leading to a template of minimal height. Finally, the drawing process of th…
Impulsive control is used to suppress the chaotic behavior in an one-dimensional discrete supply and demand dynamical system. By perturbing periodically the state variable with constant impulses, the chaos can be suppressed. It is proved analytically that the obtained orbits are bounded and periodic. Moreover, it is shown for the first time that the difference equations with impulses, used to control the chaos, can generate hidden chaotic attractors. To the best of the authors knowledge, this interesting feature has not yet been discussed. The impulsive algorithm can be used to stabilize chaos…
In this paper, we present a scheme for uncovering hidden chaotic attrac- tors in nonlinear autonomous systems of fractional order. The stability of equilibria of fractional-order systems is analyzed. The underlying initial value problem is nu- merically integrated with the predictor-corrector Adams-Bashforth-Moulton algo- rithm for fractional-order differential equations. Three examples of fractional-order systems are considered: a generalized Lorenz system, the Rabinovich-Fabrikant system and a non-smooth Chua system.
Structure analysis of the Lorenz-84 chaotic attractor
本研究通过颜色示踪映射分析Lorenz-84吸引子的三维结构，发现其围绕周期-2空腔组织，揭示多方向拉伸的新混沌机制，并在二维分支流形上验证该结构。
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A perturbation of the parameter by a small amount $ε$ can convert an attractor from chaotic to non-chaotic or vice-versa. We call a parameter value where this can happen $ε$-uncertain. The probability that a random choice of the parameter is $ε$-uncertain commonly scales like a power law in $ε$. Surprisingly, two seemingly similar ways of defining this scaling, both of physical interest, yield different numerical value…
For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". In high-dimensional chaotic attractors, trajectories are prone to travel through quite different regions of phase space, some far more unstable than others. This heterogeneity makes predictability even more difficult than in low-dimensional homogeneous chaotic attractors. A chaotic attractor is "multi-chaotic" if every point of the attractor is arbitrarily close to periodic points with different numbers of unstable di…
On explosion of the chaotic attractor
给出了一维受驱动阻尼非谐振子的奇异吸引子在强非微扰周期驱动力的振幅发生较小变化时发生突然剧烈爆炸的例子。利用平均最大李雅普诺夫指数${\bar λ}$和$q=-4$的分形维数$D_{q}$的行为，给出了奇异吸引子爆炸的唯象刻画.结果表明，爆炸奇异吸引子的建立伴随着最大平均李雅普诺夫指数${\bar λ}$的近似线性增长.当爆炸从由空相空间区域分隔的不相交的聚束组成的吸引子开始时，检测到分形维数$D_{-4}$的突然跳跃。
Lag synchronization and scaling of chaotic attractor in coupled system
本文提出了一种用于两个单向耦合混沌振子滞后同步的延迟耦合设计。在耦合的定义中引入延迟项，以针对驱动器和响应之间的任何期望的滞后。利用Hurwitz矩阵稳定性保证了滞后同步的稳定性。在存在滞后的情况下，我们能够扩大或缩小响应系统中驱动吸引子的大小。这允许在通过延迟线传输期间补偿信号幅度的衰减。延迟耦合的3D系统，Hindmarsh-Rose神经元模型，Rössler系统和Sprott系统和4D系统的数值例子说明。我们在电子电路中实现了耦合，以实现任何期望的混沌振荡器的滞后同步和吸引子的缩放。
We consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems, they are respon…
Design of time delayed chaotic circuit with threshold controller
设计了一种具有单涡卷和双涡卷复杂混沌吸引子的新型时滞混沌振子。该电路仅由几个运算放大器和二极管组成，并采用阈值控制器以提高灵活性。它有效地实现了分段线性函数。分段线性函数的控制有利于控制吸引子的形状。通过数值模拟和硬件实验构建吸引子的相图，证明了这一点。在此基础上，我们发现该电路只需引入更多的阈值就可以产生多涡卷混沌吸引子。
Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors
研究了有限区域上混沌吸引子的Poincare常返性。与标准情况相反，在回归区域的大小趋于零的情况下，该测度不再仅仅由其内部的不稳定周期轨道支持，而且还由位于该区域之外的其他特殊回归轨道支持。后者的存在导致偏离的Poincare第一返回时间的分布从泊松。因此，通过考虑这些经常性轨迹的贡献，可以提供对测量的校正估计。这具有广泛的实验意义，因为在实验室中，所有的回报只能在有限大小的区域内观察到。
Templex: a bridge between homologies and templates for chaotic attractors
Templex 通过结合细胞复形与有向图，为混沌吸引子提供更精确的拓扑描述和分类方法。
The destruction of a chaotic attractor leading to rough changes in the dynamics of a dynamical system is studied. Local bifurcations are characterised by a single or a pair of characteristic exponents crossing the imaginary axis. The approach of such bifurcations in the presence of noise can be inferred from the slowing down of the correlation decay. On the other hand, little is known about global bifurcations involving high-dimensional attractors with positive Lyapunov exponents. The global stability of chaotic attractors may be characterised by the spectral properties of the Koopman or the t…
Unidirectionally coupled Lorenz systems in which the drive possesses a chaotic attractor and the response admits two stable equilibria in the absence of the driving is under investigation. It is found that double chaotic attractors coexist in the dynamics. The approach is applicable for chains of coupled Lorenz systems. The existence of four chaotic attractors in three coupled Lorenz systems is also demonstrated.
Discontinuous Attractor Dimension at the Synchronization Transition of Time-Delayed Chaotic Systems
研究了具有时滞耦合的混沌单元网络在向完全同步过渡时的吸引子维数。特别是，我们确定的Kaplan-Yorke维数从迭代映射和两个耦合的半导体激光器的李雅普诺夫指数的频谱。我们认为，Kaplan-Yorke维数必须是不连续的过渡，并比较它的相关维数。对于一个伯努利映射系统，我们确实发现了关联维数的跳跃。在Kaplan-Yorke维数的不连续性的大小计算网络的伯努利单位作为网络大小的函数。此外，Kaplan-Yorke维数以及Kolmogorov熵与系统的大小和时间延迟的标度进行了研究。
Estimating short-time period to break different types of chaotic modulation based secure communications
近年来，混沌吸引子在保密通信系统的设计中得到了广泛的应用。传输信息信号的优选方式之一是二进制混沌调制，其中二进制消息调制混沌发生器的参数。本文提出了一种基于估计调制混沌吸引子产生的密文短周期的攻击方法。通过计算然后对发送信号的短时间周期进行滤波，可以获得具有高精度的二进制信息信号，而不需要对底层混沌系统的参数有任何了解。该方法已成功地应用于文献中提出的基于不同混沌吸引子的保密通信系统。
Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With logic output 0 or 1 mapped to dynamical attractors bounded in distinct regions of phase space, and logic inputs encoded by a very small bias parameter, we explicitly demonstrate that the system hops consistently in response to an external input stream, operating effectively as a reliable logic gate. This system offers the advantage that very low-amplitude inpu…
Embeddings of low-dimensional strange attractors: Topological invariants and degrees of freedom
当低维混沌吸引子嵌入三维空间时，其拓扑性质与嵌入有关。我们发现，只有三个拓扑性质，依赖于嵌入：奇偶校验，全球扭转，和结类型。我们讨论了它们如何随着嵌入而变化。最后，我们表明，负责创建混沌行为的机制是所有嵌入的不变量。这些结果只适用于混沌吸引子的亏格之一，其中包括大多数的情况下，实验数据进行了拓扑分析。这意味着从以前的分析中得出的结论，例如产生混沌行为的机制是Smale马蹄机制，反向马蹄机制，gateau roule，S模板分支流形，...，不是为分析选择的嵌入的伪影。
Poincaré recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to understand how chaotic attractors are shaped by singular sets of the differential equations governing the dynamics, flow curvature manifolds are computed. We show that the time dependent components of such manifolds structure Rossler-like chaotic attractors and may explain some limitation in the development of chaotic regimes.
Random attractors are the time-evolving pullback attractors of stochastically perturbed, deterministically chaotic dynamical systems. These attractors have a structure that changes in time, and that has been characterized recently using {\sc BraMAH} cell complexes and their homology groups. This description has been further improved for their deterministic counterparts by endowing the cell complex with a directed graph, which encodes the order in which the cells in the complex are visited by the flow in phase space. A templex is a mathematical object formed by a complex and a digraph; it provi…
Statistical Complexity of Sampled Chaotic Attractors
我们分析了采样混沌吸引子的统计复杂度与熵平面表示作为采样周期τ的函数。它表明，如果Bandt和Pompe程序被用来分配一个概率分布函数（PDF）的相关的时间序列，统计复杂性措施（SCM）达到一个明确的最大值为一个特定的采样周期tM。如果使用通常的直方图方法来将PDF分配给时间序列，SCM在任何采样周期τ都几乎保持不变。tM的意义进一步研究，通过比较它与文献中给出的两个主要的重建过程的典型时间：在延迟时间嵌入的Takens的一个，和确切的Nyquist-Shannon重建。结果表明，tM与Takens重建中推荐的适当延迟时间是一致的。所报道的结果对应于三个具有代表性的混沌系统具有关联维数2 < D2 < 3。最近的一个实验证实了这里提出的分析。
In this paper we present an analytical study on the synchronization dynamics observed in unidirectionally-coupled quasiperiodically-forced systems that exhibit Strange Non-chaotic Attractors (SNA) in their dynamics. The SNA dynamics observed in the uncoupled system is studied analytically through phase portraits and poincare maps. A difference system is obtained by coupling the state equations of similar piecewise linear regions of the drive and response systems. The mechanism of synchronization of the coupled system is realized through the bifurcation of the eigenvalues in one of the piecewis…
Violation of hyperbolicity via unstable dimension variability in a chain with local hyperbolic chaotic attractors
考虑一个通过扩散耦合的双曲型混沌振子链。当耦合较强时，链是同步的，并表现出双曲混沌，从而存在一个正的李雅普诺夫指数。随着耦合的衰减，第二和第三李雅普诺夫指数同时趋于零。第二个变为正值，而第三个保持接近于零。它的有限时间数值近似波动改变耦合参数的范围内的符号。这些波动出现由于不稳定的尺寸可变性，这是已知的非双曲性的来源。我们提供了一个详细的研究，这种过渡使用的方法的李雅普诺夫分析。
Escaping from nonhyperbolic chaotic attractors
研究了非双曲系统中噪声诱导的混沌吸引子逃逸过程。我们提供了一个一般的机制，在低噪声限制逃逸，采用大波动理论。具体来说，这是通过求解辅助哈密顿系统的变分方程，并通过将混沌吸引子的初始条件明确。我们的结果与H{é}non和Ikeda映射的例子，并可以直接实施的实验数据。
One-dimensional Bernoulli mapping with hole is suggested to describe the regularities of the appearance of a chaotic set under the saddle-node scenario of the birth of the Smale--Williams hyperbolic attractor. In such a mapping, a non-trivial chaotic set (with non-zero Hausdorff dimension) arises in the general case as a result of a cascade of period-adding bifurcations characterized by geometric scaling both in the phase space and in the parameter space. Numerical analysis of the behavior of models demonstrating the saddle-node scenario of birth of a hyperbolic chaotic Smale--Williams attract…
Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near eq…
Delay as an energy regulator of the generation of deterministic chaos in hydrodynamic systems with limited excitation
研究揭示延迟对限制激励下流体系统确定性混沌生成的关键作用，通过延迟调节可实现吸引子类型转换。
Tensor-Based Chaotic Perception
本文提出基于张量的混沌感知方法，利用三阶张量映射输入为混沌序列，通过吸引子拓扑指纹实现对象识别，并在Sonar和KTH-TIPS2-a数据集上验证了类别区分与感知恒常性。
Chaotic and pseudochaotic attractors of perturbed fractional oscillator
考虑一类具有α阶分数阶导数的非线性振子.在周期力的作用下，系统表现出混沌运动，称为分数阶混沌吸引子（FCA）。FCA相比，“常规”的混沌吸引子。FCA的性质进行了讨论，并证明了“伪混沌”的情况下。
In this work, the dynamical behaviors of a low-dimensional model, which governs the interplay between a driver associated with pressure gradient and relaxation of instability due to magnetic field perturbations, are investigated. Besides that, two nonlinear controllers are constructed precisely to shift the equilibria of the plasma model apart from each other. Simulation results show that shifting the equilibria can change the spacing of chaotic attractors, and subsequently break the butterfly wings into one or two symmetric pair of coexisting chaotic attractors. Furthermore, stretching the eq…
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