Publications

On decentralized adaptive pinning synchronization of complex dynamical networks

In this paper, we propose a decentralized adaptive pinning control scheme for synchronization of undirected networks using a local adaptive strategy to determine both coupling strengths and feedback gains. By applying this local adaptive strategy, we show that the network can achieve synchronization with small coupling strengths and feedback gains. We provide some simulations to verify and illustrate the theoretical results.

Finding and Analyzing the Solutions of Singular Nonlinear Traveling Wave Equations: A Dynamical Systems Approach

This overview paper reviews a dynamical systems approach to studying the singular nonlinear traveling wave equations. First, the notion of exact peakon, periodic peakon, pseudo-peakon, as well as compacton solutions for the generalized Camassa–Holm (CH) equation and the Degasperis–Procesi (DP) equation, is introduced. Based on the method of dynamical systems and the theory of singular traveling wave equations, the exact explicit parametric representations of the solutions of the above-mentioned equations are derived. These solutions show that peakon is a limit solution of a family of periodic peakons or a limit solution of a family of pseudo-peakons in different limit senses, whereas the pseudo-peakon and pseudo-periodic peakon families are smooth classical solutions in two different time scales. Second, nonlinear wave equation models are introduced to show that there exist various exact explicit peakon solutions, which are different from the peakon solution given by the generalized CH equation and the DP equation. Third, the so-called “peakon equations” discussed in some studies actually have no peakons. Corresponding to these “peakon equations”, their traveling wave systems are singular traveling wave systems of the second kind, which cannot have peakon solutions. Finally, an application example is presented to illustrate our theory and methodology using a model of nonlinear elastodynamics of materials with strong ellipticity.

<i>Lₚ</i>-Stability of a Class of Volterra Systems

This brief presents some new and explicit stability results for Volterra systems based on two different approaches. The first approach is based on monomial domination of the Volterra system's memoryless output nonlinearity and the second on its Lipschitz-norm. The former yields more widely applicable results, but introduces nonconvexity in the signal spaces to be dealt with for certain parameter values.

The Cipher Code Parameter Selection and Its Impact on Output Cycles

This paper gives the circuit design for logistic digital chaotic system, with the analysis of parameter selection for logistic cipher code, effecting factors and calculating method of sequence cycle. Through experiments it is shown that different calculating precisions and u value can be the factor that effects the cycle period most, changing u value can change the cycle and the larger precision can get the bigger cycle basically. For one thing, fixing u value and precision to test the effect of the initial value and find some good precisions; for another, further research shows there are some small cycles in good precisions. Therefore, it is unsafe to use initial value directly as the cipher code, for which the paper supposes an improvement program. This paper tests the cycle under certain conditions, and firstly deduces the cycle calculation formula, proposes the main conditions of cycles effected by the digital chaoic sequences and the cycle calculation method, then gives the scatter gram of precision-u-cycle. The methods given above have actual significances for estimating chaotic sequence cycle of finite precision in assured chaotic application field.

Kalman Filtering for Interval Systems

No abstract is provided for this article.

FEEDBACK CONTROL OF LYAPUNOV EXPONENTS FOR DISCRETE-TIME DYNAMICAL SYSTEMS

A simple, yet mathematically rigorous feedback control design method is proposed in this paper, which can make all the Lyapunov exponents of the controlled system strictly positive, for any given n-dimensional dynamical system that could be originally nonchaotic or even asymptotically stable. The argument used is purely algebraic and the design procedure is completely schematic, with no approximations used throughout the derivation. This is a rigorous and convenient technique suggested as an attempt for anticontrol of chaotic dynamical systems, with explicit computational formulas derived for applications.

Secondary Control of Microgrids

BIFURCATION ANALYSIS OF CHEN'S EQUATION

Anticontrol of chaos by making a nonchaotic system chaotic has led to the discovery of some new chaotic systems, particularly the continuous-time three-dimensional autonomous Chen's equation with only two quadratic terms. This paper further investigates some basic dynamical properties and various bifurcations of Chen's equation, thereby revealing its different features from some other chaotic models such as its origin, the Lorenz system.

Distributed<i>H</i>_∞consensus of multi-agent systems: a performance region-based approach

This article addresses the distributed H ∞ consensus problem of multi-agent systems with general linear node dynamics using relative output measurements. The notion of H ∞ consensus performance region is first introduced and then analysed as a basis for the protocol design. A new kind of distributed observer-type H ∞ protocols is further proposed. Theoretical analysis indicates that the distributed H ∞ consensus problem can be solved if and only if the coupling strength of the protocol belongs to the H ∞ performance region of the closed-loop network. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Model conversions of uncertain linear systems using interval multipoint Pade approximation

Many dynamic systems and industrial control processes can be represented by a multirate sampled-data uncertain system, which consists of a continuous-time uncertain subsystem and a multirate discrete-time uncertain subsystem. The uncertainties in these systems arise from unmodeled dynamics, parameter variations, sensor noises, actuator constraints, etc. As is the common practice the sampled-data uncertain system needs to be converted to a purely continuous-time or discrete-time uncertain model, so that the well-established analysis and design methods in the continuous-time or discrete-time domain can be directly applied to the equivalent model. This paper presents a new interval multipoint Pade approximation method for converting a continuous-time (discrete-time) uncertain linear system to an equivalent discrete-time (continuous-time) uncertain model. The system matrices characterizing the state-space descriptions of the original uncertain systems are represented by interval matrices. Using the approximate uncertain models obtained based on interval analysis and multipoint Pade approximation the dynamic states of the resulting models have been shown to be able to closely match those of the original uncertain systems for a relatively longer sampling period.

Dual-wavelength chaos generation and synchronization in erbium-doped fiber lasers

Dual-wavelength chaos is generated in one erbium-doped fiber laser. Tunable optical filters (TOF) are used to select the wavelengths. The generation of chaos is achieved by either modulating the pump laser diode near the relaxation oscillation frequency of the fiber laser or by introducing the modulation through an electrooptic modulator built into each wavelength branch. The receiver is fabricated with identical parameters as the transmitter except for an open loop structure. By tuning the TOF in the receiver, synchronization of chaos is observed in either of the two wavelengths. Thus, it can pave the way for wavelength-division-multiplexing chaos communications.

Reweighted Alternating Direction Method of Multipliers for DNN weight pruning

As Deep Neural Networks (DNNs) continue to grow in complexity and size, leading to a substantial computational burden, weight pruning techniques have emerged as an effective solution. This paper presents a novel method for dynamic regularization-based pruning, which incorporates the Alternating Direction Method of Multipliers (ADMM). Unlike conventional methods that employ simple and abrupt threshold processing, the proposed method introduces a reweighting mechanism to assign importance to the weights in DNNs. Compared to other ADMM-based methods, the new method not only achieves higher accuracy but also saves considerable time thanks to the reduced number of necessary hyperparameters. The method is evaluated on multiple architectures, including LeNet-5, ResNet-32, ResNet-56, and ResNet-50, using the MNIST, CIFAR-10, and ImageNet datasets, respectively. Experimental results demonstrate its superior performance in terms of compression ratios and accuracy compared to state-of-the-art pruning methods. In particular, on the LeNet-5 model for the MNIST dataset, it achieves compression ratios of 355.9 × with a slight improvement in accuracy; on the ResNet-50 model trained with the ImageNet dataset, it achieves compression ratios of 4.24 × without sacrificing accuracy.

Trapping in dendrimers and regular hyperbranched polymers

Dendrimers and regular hyperbranched polymers are two classic families of macromolecules, which can be modeled by Cayley trees and Vicsek fractals, respectively. In this paper, we study the trapping problem in Cayley trees and Vicsek fractals with different underlying geometries, focusing on a particular case with a perfect trap located at the central node. For both networks, we derive the exact analytic formulas in terms of the network size for the average trapping time (ATT)—the average of node-to-trap mean first-passage time over the whole networks. The obtained closed-form solutions show that for both Cayley trees and Vicsek fractals, the ATT display quite different scalings with various system sizes, which implies that the underlying structure plays a key role on the efficiency of trapping in polymer networks. Moreover, the dissimilar scalings of ATT may allow to differentiate readily between dendrimers and hyperbranched polymers.

Fuzzy modeling and adaptive control of uncertain chaotic systems

A simple and systematic approach is developed for modeling and adaptive control of an unknown (or uncertain) chaotic system, using only input–output data obtained from the underlying dynamical system. Gaussian fuzzy membership functions are used in conjunction with the least-squares principle for the modeling and control. Based on the fuzzy modeling, an adaptive controller is devised, which works through self-adjusting the means and variances of the Gaussian membership functions for adaptation. The design procedure is illustrated by using the chaotic Duffing oscillator as an example, on which simulation results demonstrate the effectiveness of the proposed methodology.

Computing Cliques and Cavities in Networks

Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions. Since searching for maximum cliques is an NP-complete problem, we use k-core decomposition to determine the computability of a given network. For a computable network, we design a search method with an implementable algorithm for finding cliques of different orders, obtaining also the Euler characteristic number. Then, we compute the Betti numbers by using the ranks of boundary matrices of adjacent cliques. Furthermore, we design an optimized algorithm for finding cavities of different orders. Finally, we apply the algorithm to the neuronal network of C. elegans with data from one typical dataset, and find all of its cliques and some cavities of different orders, providing a basis for further mathematical analysis and computation of its structure and function.

A Game-Theoretic Approach to Solving the Roman Domination Problem

The Roamn domination problem is one important combinatorial optimization problem that is derived from an old story of defending the Roman Empire and now regains new significance in cyber space security, considering backups in the face of a dynamic network security requirement. In this paper, firstly, we propose a Roman domination game (RDG) and prove that every Nash equilibrium (NE) of the game corresponds to a strong minimal Roman dominating function (S-RDF), as well as a Pareto-optimal solution. Secondly, we show that RDG is an exact potential game, which guarantees the existence of an NE. Thirdly, we design a game-based synchronous algorithm (GSA), which can be implemented distributively and converge to an NE in $O(n)$ rounds, where $n$ is the number of vertices. In GSA, all players make decisions depending on the local information. Furthermore, we enhance GSA to be enhanced GSA (EGSA), which converges to a better NE in $O(n^2)$ rounds. Finally, we present numerical simulations to demonstrate that EGSA can obtain a better approximate solution in promising computation time compared with state-of-the-art algorithms.

Controllability of Networked Sampled-Data Systems With Time Delays

This article investigates the controllability of networked sampled-data systems with various time delays on both control and transmission channels. Necessary and sufficient controllability conditions are first derived for systems with a single delay and then extended to systems with multiple delays. It is found that delays in control signals have no effects on the overall controllability. For a networked system whose topology matrix has only zero eigenvalues, delays of neither control nor transmission signals will affect the overall controllability. It is proved that an uncontrollable mode 1 of such a networked sampled-data system cannot be altered by arbitrary delays. Finally, the networked sampled-data system with first-order holders is discussed, which is modeled as a variant of time-delayed system, and some easy-to-verify algebraic conditions on the controllability are given based on matrix rank checking.

[From the Editor]

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