Perceptron is one of the most important aspects of artificial neural networks (ANN), while cellular neural networks (CNN) are biologically inspired systems in which computation emerges from the collective behavior of some locally coupled simple cells. However, whether the minimal number of the neurons in the hidden layer of a perceptron needed or a CNN template design for performing a prescribed task has not been completely characterized today. This article summarizes several algorithms for decomposing linearly non-separable Boolean function, specially a DNA-like decomposing algorithm and a shortest distance decomposing algorithm, with emphasis on the relationship between universal perceptron (UP) and CNN, and provides some examples to show the powerful ability of these algorithms in decomposing non-LSBF. Moreover, a new concept named CNN-UP is developed, which may lead to a useful new PC software in designing CNN and perceptron in the near future.
In this article, dynamical robustness of a directed complex network with additive noise is inverstigated. The failure of a node in the network is modeled by injecting noise into the node. Under the framework of mean-square stochastic stability, a new robustness metric is formulated to characterize the robustness of the network in terms of synchronization to the additive noise. It is found that the node dynamics plays a pivotal role in dynamical robustness of the directed network. Numerical simulations are shown for illustration and verification.
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In this paper, a problem in feedback control of limit cycle amplitudes is studied. A graphical approach for this bifurcation control problem is developed by means of higher-order harmonic balance approximations for both amplitude and frequency of the system oscillatory outputs. The approach starts with the familiar Hopf bifurcation mechanism, and employs the second, fourth, and sixth-order harmonic balance approximations to generate a sequence of graphical tests for convergence analysis of the system oscillatory outputs. This sequential graphical testing leads to accurate approximations of limit cycles of small amplitudes in the system outputs. Degenerate Hopf bifurcation theory is used to formulate an appropriate control objective of capturing small-amplitude limit cycles, which can avoid reaching unstable equilibria or other undesirable limit sets. A rich cubic planar model is presented for illustration of the proposed control method.
In this paper, we derive a fractional mean-value theorem both in the sense of Riemann–Liouville and in the sense of Caputo. This new formulation is more general than the generalized Taylor's formula of Kolwankar and the fractional mean-value theorem in the sense of Riemann–Liouville developed by Trujillo.
This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.
This article presents an overview on the state-of-the-art development in complex network controllability and its robustness against malicious attacks and random failures. Specifically, it first reviews the concepts of network pinning control and controllability, and then discusses the network controllability robustness against destructive attacks by means of node- and/or edge-removal. The related issue of network connectivity robustness is also discussed. To that end, it furthermore provides an brief overview on the recent development of a machine-learning approach for predicting optimal network controllability robustness, which may shed some lights on the understanding of optimal network structures for various design considerations.
摘要 提出了参数开关调制控制混沌方法,通过对蔡氏电路中的电容参数进行开关调制,可把蔡氏电路由混沌状态控制到其平衡态和nP周期轨道.数值模拟和电路仿真的结果证实了本方法的有效性,丰富了蔡氏电路的工程应用方法 关键词: 混沌控制 / 蔡氏电路 / 参数开关调制 Abstract Keywords: / / 作者及机构信息 罗晓曙4, 汪秉宏3, 陈关荣2, 蒋品群1, 方锦清5, 全宏俊3 (1)广西师范大学物理与电子科学系,桂林541004;; (2)香港城市大学电子工程系,香港九龙; (3)中国科学技术大学近代物理系,合肥230026; (4)中国科学技术大学近代物理系,合肥230026,广西师范大学物理与电子科学系,桂林541004; (5)中国原子能科学研究院,北京102413 基金项目: 广西自然科学基金 (批准号 :0 135 0 6 3);国家重点基础研究专项基金 ( 973计划 );国家攀登计划“非线性科学”;国家自然科学基金 (批准号 :19932 0 2 0,199740 39,5 9876 0 39,19875 0 80 ,70 0 710 47);香港特区政府研究资助局基金 (RGC CUHK42 41 0 1P); Authors and contacts Luo Xiao-Shu4, Wang Bing-Hong3, Chen Guan-Rong2, Jiang Pin-Qun1, Fang Jin-Qing5, Quan Hong-Jun3 (1)广西师范大学物理与电子科学系,桂林541004;; (2)香港城市大学电子工程系,香港九龙; (3)中国科学技术大学近代物理系,合肥230026; (4)中国科学技术大学近代物理系,合肥230026,广西师范大学物理与电子科学系,桂林541004; (5)中国原子能科学研究院,北京102413 参考文献 施引文献
This paper studies a class of coupled Van der Pol (CVDP) cellular neural networks (CNNs) that can be realized via a coupled fourth-order circuit with two synaptic currents. The local activity theory, developed by Chua in 1997, is applied to study the CVDP CNN, thereby revealing that the bifurcation diagram of the CVDP CNN has a local activity domain with an edge of chaos, as well as a one-dimensional locally passive domain. Although no chaotic phenomena have been identified in simulations, many complex dynamical behaviors have been observed, such as the co-existence of one-periodic, divergent, and convergent orbits, at the edge of chaos.
This technical note addresses the distributed fixed-time consensus protocol design problem for multi-agent systems with general linear dynamics over directed communication graphs. By using motion planning approaches, a class of distributed fixed-time consensus algorithms are developed, which rely only on the sampling information at some sampling instants. For linear multi-agent systems, the proposed algorithms solve the fixed-time consensus problem for any directed graph containing a directed spanning tree. In particular, the settling time can be off-line pre-assigned according to task requirements. Compared with the existing results for multi-agent systems, to our best knowledge, it is the first-time to solve fixed-time consensus problems for general linear multi-agent systems over directed graphs having a directed spanning tree. Extensions to the fixed-time formation flying are further studied for multiple satellites described by Hill equations.
This paper introduces an optimal fuzzy proportional-integral-derivative (PID) controller for a solar power plant. The fuzzy PID controller is a discrete-time version of the conventional PID controller, which preserves the same linear structure of the proportional, integral, and derivative parts but has constant coefficient, self-tuned control gains. The constant PID control gains and other control parameters are optimized by using the multiobjective generic algorithm (GA), thereby yielding an optimal fuzzy PID controller.
This paper proposes a systematic methodology for creating multifolded torus chaotic attractors from a simple three-dimensional piecewise-linear system. Theoretical analysis shows that the multifolded torus chaotic attractors can be generated via alternative switchings between two basic linear systems. The theoretical design principle and the underlying dynamic mechanism are then further investigated by analyzing the emerging bifurcation and the stable and unstable subspaces of the two basic linear systems. A novel block circuit diagram is also designed for hardware implementation of 3-, 5-, 7-, 9-folded torus chaotic attractors via switching the corresponding switches. This is the first time a 9-folded torus chaotic attractor generated by an analog circuit has been verified experimentally. Furthermore, some recursive formulas of system parameters are rigorously derived, which is useful for improving hardware implementation.
Cross-border equity and long-term debt securities portfolio investment networks are analysed from 2002 to 2012, covering the 2008 global financial crisis. They serve as network-proxies for measuring the robustness of the global financial system and the interdependence of financial markets, respectively. Two early-warning indicators for financial crises are identified: First, the algebraic connectivity of the equity securities network, as a measure for structural robustness, drops close to zero already in 2005, while there is an over-representation of high-degree off-shore financial centres among the countries most-related to this observation, suggesting an investigation of such nodes with respect to the structural stability of the global financial system. Second, using a phenomenological model, the edge density of the debt securities network is found to describe, and even forecast, the proliferation of several over-the-counter-traded financial derivatives, most prominently credit default swaps, enabling one to detect potentially dangerous levels of market interdependence and systemic risk.
This paper introduces the notion of chaos synthesis by means of evolutionary algorithms and develops a new method for chaotic systems synthesis. This method is similar to genetic programming and grammatical evolution and is being applied along with three evolutionary algorithms: differential evolution, self-organizing migration and genetic algorithm. The aim of this investigation is to synthesize new and "simple" chaotic systems based on some elements contained in a prechosen existing chaotic system and a properly defined cost function. The investigation consists of eleven case studies: the aforementioned three evolutionary algorithms in eleven versions. For all algorithms, 100 simulations of chaos synthesis were repeated and then averaged to guarantee the reliability and robustness of the proposed method. The most significant results were carefully selected, visualized and commented in this report.
The paper deals with the steady state bifurcations of the Kuramoto–Sivashinsky (K–S) equation in two spatial dimensions with zero mean and periodic boundary value conditions. Applying the perturbation method, asymptotic expressions of the steady state solution branches that have bifurcated from the equilibrium are obtained. Furthermore, stability of the bifurcated solution branches is discussed.
