2,312 publications from this institution
Over the last two decades, generating complex multi-scroll chaotic attractors via simple electronic circuits or simple systems has seen rapid development. This paper provides a brief overview of the subject on multi-scroll chaotic attractors generation, including some fundamental theories and design methodologies.
Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. Analytical results show that every layer therein is a sparse and heterogeneous subnetwork with a scale-free topology. Counterintuitively, every layer has an extremely strong controllability in spite of its scale-free structure that is usually difficult to control. Another amazing feature is that the controllability is robust against targeted attacks to critical nodes but vulnerable to random failures, which also differs from ordinary scale-free networks. The multi-chain structure with a small number of chain roots arising from each layer accounts for the strong controllability and the abnormal feature. The multiplex congruence network offers a graphical solution to the simultaneous congruences problem, which may have implication in cryptography based on simultaneous congruences. Our work also gains insight into the design of networks integrating advantages of both heterogeneous and homogeneous networks without inheriting their limitations.
This paper is concerned with the synchronization of multiagent systems connected via different types of interactions, known as multilayer networks. Additive coupling and Markovian switching coupling are proposed to capture the layered connections with two kinds of mathematical models constructed. First, based on simultaneously diagonalization of multiple Laplacian matrices, a general criterion is derived, ensuring that the synchronization problem with additive coupling can be decoupled. Then, an alternative condition is presented, which is related to the number of layers, regardless of the number of agents. With the derived criteria, a concept of joint synchronization region is introduced and further discussed as a network design problem. Synchronization with Markovian switching layers is also analyzed in parallel, exemplified by some special cases of two-layer networks. Finally, a group of cellular neural networks coupled by two-layer connections are chosen to illustrate the effectiveness of the theoretical results.
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A fuzzy logic-based approach is taken in this paper for modeling, prediction, and predictive control of unknown or uncertain chaotic systems. Only output data of the underlying system are required. A fuzzy predictive framework using a general structure of a linear combination of Gaussian basis functions is developed, where the basis functions are expressed as probability density functions and are empirically determined from the time-series data. A real-time one-pass learning algorithm is developed for identification of the chaotic system. Based on this framework, a fuzzy predictive controller is designed, which is especially suitable for sparse data in a real-time environment. Several simulation examples are then given for demonstration.
We study Bode and Poisson type integral relations. We focus on a link between the well-known argument principle and Bode and Poisson integrals, which have been unnoticed previously. We show how various integral constraints may be unified under an extended version of the argument principle. This enables us to derive the classical Bode and Poisson integral relations in a simple manner, and further to discover new integral formulas of significance for an analysis of control design limitation and tradeoff.
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It has been argued that chaotic vibration provides the best possibility for achieving efficient and thorough mixing of fluids, by evoking complex and abundant perturbations into the original steady flows. In the last two decades, advances in the understanding of chaos theory and nonlinear-circuit technologies have led to favorable prospects to capitalize some features of chaos in liquid mixing applications. In this paper, a liquid mixing apparatus (an electromechanical shaker) based on the commonly used stirred tank model is introduced. The design and implementation of this liquid shaker, capable of working under the control of different kinds of signals, are reported. Constant-voltage signals, periodic signals and chaotic/hyperchaotic signals are applied to the impeller/tank velocity control mechanisms, exploring the efficacy of different perturbation schemes for liquid mixing. Comparable experiments are carried out to investigate the time consumption in sucrose dissolving processes and the dye dispersion homogeneity in visualizable mixing flows. The results of these experiments reveal that chaotic and hyperchaotic perturbations help enhance the liquid mixing efficiency and homogeneity quite significantly, yielding faster and more uniform results than all nonchaotic counterparts.
This paper presents a mathematically rigorous proof for the existence of chaos in a modified Lorenz system using the theory of Shil'nikov bifurcations of homoclinic and heteroclinic orbits. Together with its dynamical behaviors, which have been extensively studied, the chaotic dynamics of the modified Lorenz system are now much better understood, providing a rigorous theoretic foundation to support studies and applications of this important class of chaotic systems.
In this paper, a four-dimensional (4D) continuous-time autonomous hyperchaotic system with only one equilibrium is introduced and analyzed. This hyperchaotic system is constructed by adding a linear controller to the second equation of the 3D Lorenz system. Some complex dynamical behaviors of the hyperchaotic system are investigated, revealing many interesting properties: (i) existence of periodic orbit with two zero Lyapunov exponents; (ii) existence of chaotic orbit with two zero Lyapunov exponents; (iii) chaos depending on initial value w 0 ; (iv) chaos with only one equilibrium; and (v) hyperchaos with only one equilibrium. Finally, two complete mathematical characterizations for 4D Hopf bifurcation are derived and studied.
GIS (Gas-Insulated Switchgear) equipment generates multi-band partial discharge, electromagnetic vibration, acoustic emission and other signals during operation. Existing single-mode analysis is difficult to accurately identify complex faults, and the false alarm and missed alarm rates are high. A multi-frequency signal feature cascade network is proposed. Through frequency band decomposition, deep feature extraction and fusion attention mechanism, the early and accurate assessment of GIS sub-health status can be achieved, thereby improving the operation safety and equipment life. In this study, the original discharge, electromagnetic vibration and acoustic emission signals are first decomposed by Daubechies4 wavelet packet, and the signals are divided into three frequency bands: low, medium and high. Then, they are input into the corresponding branches. Subsequently, each branch uses convolutional neural network and self-attention module to collaboratively extract weak fault features in time domain and frequency domain. Next, the features output by each frequency band branch are cascaded in the channel dimension, and the redundancy is compressed and the key frequency band information is strengthened by fusion attention mechanism. Parameter sharing and network pruning technology based on L₁ norm are used to achieve model lightweight while maintaining accuracy. Finally, with the help of transfer learning and adversarial training framework, GIS data of different manufacturers and models are fine-tuned and optimized. Experiments show that under 5-fold cross validation, the proposed model has an F1 score of 0.923 and an AUCof 0.897, which is significantly better than baseline models such as ResNet-18 and SVM. In the detection of key faults such as partial discharge, the average warning time is 62.3 minutes and the detection rate exceeds 98%. In addition, the single sample delay of the model on the platform is only 29.9ms, which meets the real-time requirements. The results show that this method has high recognition accuracy, strong real-time and environmental adaptability, and is suitable for actual GIS sub-health monitoring.
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This paper studies general higher order distributed consensus protocols in multiagent dynamical systems. First, network synchronization is investigated, with some necessary and sufficient conditions derived for higher order consensus. It is found that consensus can be reached if and only if all subsystems are asymptotically stable. Based on this result, consensus regions are characterized. It is proved that for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> th-order consensus, there are at most ⌊( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> +1)/2⌋ disconnected stable and unstable consensus regions. It is shown that consensus can be achieved if and only if all the nonzero eigenvalues of the Laplacian matrix lie in the stable consensus regions. Moreover, the ratio of the largest to the smallest nonzero eigenvalues of the Laplacian matrix plays a key role in reaching consensus and a scheme for choosing the coupling strength is derived. Furthermore, a leader-follower control problem in multiagent dynamical systems is considered, which reveals that to reach consensus the agents with very small degrees must be informed. Finally, simulation examples are given to illustrate the theoretical analysis.
A novel non-coherent multi-level differential chaos shift keying (DCSK) modulation scheme is proposed in this paper. This new scheme is based on both the transmitted-reference technique and M-ary orthogonal modulation, where each data-bearing signal is chosen from a set of orthogonal chaotic wavelets constructed by a reference signal. Thanks to this signaling design, the new scheme can achieve a higher attainable data rate, lower energy loss in reference transmission, increased bandwidth efficiency, better data security and better bit error rate (BER) performance as compared to the conventional DCSK. Unlike other DCSK-based systems that separate the reference and data-bearing signals using the TDMA scheme, this new system employs I/Q channels to send these two signals in a parallel and simultaneous manner, making the system easily extendable to multi-carriers. This transmission mechanism not only can further increase data rate but also can remove all radio frequency delay lines from detectors. Analytical BER expressions of the proposed system are derived for both additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. Relevant simulation results are given and compared to non-coherent binary/M-ary DCSK systems. In addition, the impacts of various system parameters on noise performance are discussed. Both theoretical analysis and simulation results confirm the promising benefits of the new design.
In network science, the non-homogeneity of node degrees has been a concerned issue for study. Yet, with the modern web technologies today, the traditional social communication topologies have evolved from node-central structures to online cycle-based communities, urgently requiring new network theories and tools. Switching the focus from node degrees to network cycles, it could reveal many interesting properties from the perspective of totally homogeneous networks, or sub-networks in a complex network, especially basic simplexes (cliques) such as links and triangles. Clearly, comparing to node degrees it is much more challenging to deal with network cycles. For studying the latter, a new clique vector space framework is introduced in this paper, where the vector space with a basis consisting of links has the dimension equal to the number of links, that with a basis consisting of triangles has the dimension equal to the number of triangles, and so on. These two vector spaces are related through a boundary operator, e.g., mapping the boundary of a triangle in one space to the sun of three links in the other space. Under the new framework, some important concepts and methodologies from algebraic topology, such as characteristic number, homology group and Betti number, will have a play in network science leading to foreseeable new research directions. As immediate applications, the paper illustrates some important characteristics affecting the collective behaviors of complex networks, some new cycle-dependent importance indexes of nodes, and implications for network synchronization and brain network analysis.
