Publications

Distributed discrete-time convex optimization with closed convex set constraints: Linearly convergent algorithm design

<p>The convergence rate and applicability to directed graphs with interaction topologies are two important features for practical applications of distributed optimization algorithms. In this paper, a new kind of fast distributed discrete-time algorithms is developed for solving convex optimization problems with closed convex set constraints over directed interaction networks. Under the gradient tracking framework, two distributed algorithms are respectively designed over balanced and unbalanced graphs, where momentum terms and two time-scales are involved. Furthermore, it is demonstrated that the designed distributed algorithms attain linear speedup convergence rates provided that the momentum coefficients and the step-size are appropriately selected. Finally, numerical simulations verify the effectiveness and the global accelerated effect of the designed algorithms.</p>

Sensitivity and transitivity of fuzzified dynamical systems

In this paper, it is proved that a set-valued dynamical system is sensitively dependent on initial conditions (resp., F -sensitive, multi-sensitive) if and only if its g-fuzzification is sensitively dependent on initial conditions (resp., F -sensitive, multi-sensitive), where F is a Fürstenberg family. As an application, it is shown that there exists a sensitive dynamical system whose g-fuzzification does not have such sensitive dependence for any g in a certain domain. Moreover, a sufficient condition is derived for ensuring that the g-fuzzification of every nontrivial dynamical system is not transitive.

Effect of large buffers on TCP queueing behavior

Using a simple model of saturated, synchronized and homogeneous sources of TCP Reno with drop-tail queue management and a discrete-time framework, we derive formulae for stationary as well as transient queueing behavior that shed light on the relationship between large buffers and work conservation (queue never empties). Using simulations, the relevance of the results for the case of non-synchronized sources is demonstrated. In particular, we demonstrate that a certain simple lower bound for the stationary queue length applies also to the case where the sources are non-stationary.

From the editor

Presents the editorial for this issue of the publication.

Complex dynamics in a permanent-magnet synchronous motor model☆

This paper characterizes the complex dynamics of the permanent-magnet synchronous motor (PMSM) model with a non-smooth-air-gap, extending the work on the smooth case studied elsewhere. The stability, the number of equilibrium points, and the pitchfork and Hopf bifurcations are analyzed by using bifurcation theory and the center manifold theorem. Numerical simulations not only confirm the theoretical analysis results but also show some more new results including the period-doubling bifurcation, cyclic fold bifurcation, single-scroll and double-scroll chaotic attractors, ribbon-chaotic attractor, as well as intermittent chaos that are different from those reported in the literature before. Moreover, analytical expressions of an approximate stability boundary are given, by computing the local quadratic approximation of the two-dimensional stable manifold at an order-2 saddle point. Combining the existing results with the new results reported in this paper, a fairly complete description of the complex dynamics of the PMSM model is now obtained.

Jittering performance of random deflection routing in packet networks

This paper reports a study of random deflection routing protocol and its impact on delay-jitter over packet networks. In case of congestion, routers with a random deflection routing protocol can forward incoming packets to links laying off shortest paths; namely, packets can be “deflected” away from their original paths. However, random deflection routing may send packets to several different paths, thereby introducing packet re-ordering. This could affect the quality of receptions, it could also impair the overall performance in transporting data traffic. Nevertheless, the present study reveals that deflection routing could actually reduce delay-jitter when the traffic loading on the network is not heavy.

Performance Analysis of the CS-DCSK/BPSK Communication System

As a spread spectrum communication system, code-shifted differential chaos shift keying (CS-DCSK) is required to provide reasonable bit error performance in a coexisting scenario where the conventional communication system is an interferer. Meantime, the bit error performance of the conventional communication system should not deteriorate dramatically in the presence of a CS-DCSK signal, which is as an interferer. This paper studies the performances of the CS-DCSK/BPSK coexisting system. By comparisons on the bit error rate (BER) of two coexisting systems, i.e., CS-DCSK/BPSK and DCSK/BPSK systems, in different channel environments at the same interference signal ratio, it reveals that CS-DCSK/BPSK has better performances than DCSK/BPSK. The BER expression of the CS-DCSK sub-system is derived in the presence of BPSK interference signals when two sub-systems are synchronized. Also derived is the BER expression of the BPSK sub-system in the presence of CS-DCSK signals when two sub-systems are asynchronized and synchronized, respectively. For the synchronization case, the BER expression of the BPSK sub-system is independent of the strengths of CS-DCSK signals. As a new interferer, CS-DCSK has less effect on the conventional communication system. It is shown that numerical simulations are in good agreement with the analytic results.

On global synchronization of chaotic systems

The paper discusses the basic problem of chaos synchronization and derives some simple yet explicit conditions for its global convergence verification.

On the Security of the Yi–Tan–Siew Chaotic Cipher

This paper presents a comprehensive analysis on the security of the Yi-Tan-Siew chaotic cipher proposed in [IEEE TCAS-I 49(12):1826-1829 (2002)]. A differential chosen-plaintext attack and a differential chosen-ciphertext attack are suggested to break the sub-key K, under the assumption that the time stamp can be altered by the attacker, which is reasonable in such attacks. Also, some security Problems about the sub-keys $α$ and $β$ are clarified, from both theoretical and experimental points of view. Further analysis shows that the security of this cipher is independent of the use of the chaotic tent map, once the sub-key $K$ is removed via the proposed suggested differential chosen-plaintext attack.

Determining the controllable conditions for time-delayed feedback chaos control

Based on Hopf bifurcation theory and methods in time-delayed systems, we ana lytically determine some general conditions of time-delayed feedback control of three-dimensional autonomous chaotic systems. With this method, a criterion for the stability of periodic solution under control and for the direction of Hopf b ifurcation is derived theoretically studied. Applying the method to the control of some three-dimensional autonomous chaotic systems, we can analytically find the cont rollable parameter in this region. Choosing parameters in it, we can successfull y stabilize chaotic orbits to periodic states.

Network analysis of dynamics of chaotic maps in digital domain

Dynamics of chaotic maps in an infinite-precision domain have been established complete mathematical framework. The case in finite-precision computer remains to be further explored. The related previous works treated a digital chaotic map as a black box and gave different explanations according to the test results of the output. Using the Logistic and Tent maps as typical examples, we disclose some dynamical properties of chaotic maps in fixed-point arithmetic by studying its corresponding state-mapping network (SMN), where every possible value is considered as a node and the mapping relation existing between any pair of nodes works as a directed edge. The scale-free properties of SMN are quantitatively proven. The obtained results can be extended to the scenario of floating-point arithmetic and to other chaotic maps. Understanding the real network structure of SMN of a chaotic map in the digital computer can facilitate counteracting dynamics degeneration of digital chaotic maps, which also help evaluate and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.

Model Predictive Flocking Control of the Cucker-Smale Multi-Agent Model With Input Constraints

This paper develops a model predictive flocking control scheme for the Cucker-Smale multi-agent model with input constraints. A decentralized controller is designed based only on neighboring measurements. Connectivity conditions are established for guaranteeing the convergence to a rigid flock. Finally, numerical simulation demonstrates the effectiveness of the control scheme.

WHAT DOES CHAOS HAVE TO DO WITH SYSTEMS AND CONTROL ENGINEERING

Experimental Verification of Multidirectional

-grid scroll with chaotic attractors is very difficult technically, signifying the novelty and significance of the achievements reported in this paper. Finally, this circuit design approach provides some principles and guidelines for hardware implementation of chaotic attractors with a multidirectional orientation and with a large number of scrolls, useful for future circuitry design and engineering applications. Index Terms—Circuit implementation, hysteresis series, multidirectional chaotic attractor, multiscroll chaotic attractor, saturated series.

Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain

In this paper, a general two-neuron model with distributed delays and a strong kernel is investigated. By applying the frequency domain approach and analyzing the associated characteristic equation, the existence of bifurcation parameter for the model is determined. Furthermore, if the mean delay used as a bifurcation parameter, it is found that Hopf bifurcation occurs for the strong kernel. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determined by the Nyquist criterion and the graphical Hopf bifurcation theorem. Some numerical simulations are given to justify the theoretical analysis results.

A Memristor-Based Chaotic System with Bifurcation Analysis

This paper proposes and investigates a memristor-based chaotic system by incorporating an HP TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> memristor into the canonical Chen's chaotic system. More precisely, a charge-controlled memristor model with some appropriate boundary conditions is introduced. The relationship between the electric charge and the flux passing through the memristor is formulated and then employed as a nonlinear term in the constructed chaotic system. The rich dynamical behaviors of the memristor-based system are demonstrated by calculating the Lyapunov exponent spectrum and Lyapunov dimension, observing the chaotic attractors, analyzing the bifurcations.

EVOLVING NETWORKS DRIVEN BY NODE DYNAMICS

In this paper, a new model of evolving networks is proposed based on the dynamical behaviors of nodes in the network. The probability that an existing node in the current network receives a new link from the newly added node is proportional to the defined "activity" of that particular node, which is equivalent to the energy signal of the system from a control theory point of view. This network is found to have the scale-free feature with the degree distribution in a power-law form. This model provides another explanation for the emergence of scale-free networks in many real-world examples.

GENERATION OF n × m-SCROLL ATTRACTORS UNDER A CHUA-CIRCUIT FRAMEWORK

In this paper, the generation of n × m-scroll attractors under a Chua-circuit framework is presented. By using a sawtooth function, f 1 (x), and a staircase function, f 2 (y), n × m-scroll attractors can be generated and observed from a third-order circuit. Its dynamical behaviors are investigated by means of theoretical analysis as well as numerical simulation. Moreover, two electronic circuits are designed for its realization, and experimental observations of n × m-scroll attractors based on Chua's circuit are reported, for the first time in the literature.