Publications

Local diversity–stability of the q-snapback network model

The diversity–stability relationship in system dynamics had found significant implication to species evolution in the classical cascade and niche models of the ecosystem. In this paper, the local diversity–stability of the q-snapback network model, which is similar to the cascade and niche models, is investigated by analyzing the eigenvalue distribution near its equilibrium. It is found that the basic diversity–stability feature of the q-snapback network is similar to that of the random-graph network, and to that of the cascade and niche models when their different degree distributions are set to be homogeneous.

A Note on Hopf Bifurcation in Chen's System

In this technical note, the Hopf bifurcation in Chen's system is studied. Some corresponding dynamics are also discussed briefly.

PowerSystems asDynamic Networks

Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay

When a transmission delay occurs in the interconnection of linearly coupled systems described by ordinary differential equations (LCODEs), both synchronization and the final synchronized state will vary. In this paper, mathematical analysis is presented on the synchronization phenomena of LCODEs with a single coupling delay. Criteria are derived for both local and global synchronization. It is known that in addition to the dynamical behaviors of the underlying uncoupled system and the coupling configuration, the coupling strength and the coupling delay also play key roles on the stability of synchronization. Both theoretical and numerical analysis indicate that under some conditions, if the coupling strength is large enough, the coupled system can be completely synchronized for any coupling delay. On the other hand, in some cases, the coupled system can be synchronized if the coupling delay is small enough.

GENERATION AND CONTROL OF SPHERICAL AND CIRCULAR ATTRACTORS USING SWITCHING SCHEMES

Construction of special (chaotic) attractors for various design demands has drawn much attention recently. This paper studies the generation of a family of spherical and circular quasi-periodic/chaotic attractors from simple switched nonlinear systems. Controllers are designed for manipulating the sizes or shapes of islands and bridges in such circular attractors. The underlying mechanism of generating these attractors from the switched systems is investigated.

LEON CHUA’S MEMRISTOR

No abstract is provided for this article.

Testing Chaos Based on Empirical Distribution Function: A Simulation Study

It is well known that many classical statistical tests of randomness generally fail to distinguish chaos generated by some lower-dimensional deterministic dynamical systems from independent and identically distributed (i.i.d.) random series. In this paper, we suggest a powerful statistical testing method based on empirical distribution function that can well detect chaos and i.i.d. random series. Keywords: ChaosEmpirical Distribution FunctionNonlinear Time SeriesSimulation StudyTest Of Randomness

Integrated fuzzy modeling and adaptive control for nonlinear systems

A systematic design methodology for integrating fuzzy modeling and adaptive control is proposed and developed in this paper. This design procedure provides a real-time system identification scheme using less fuzzy rules than that of the other existing methods due to a new sliding-mode learning mechanism embedded in the identified model, which has robust stability not only for stabilization of the identified system but also for trajectory tracking control. The integration of the identification and the adaptive control schemes ensures the suggested methodology overall advantageous and more attractive as compared to the other existing, usually separated, design approaches. Two typical complex systems are simulated, showing some convincing stabilization and tracking performance of the proposed integrated fuzzy system.

Resilient Consensus of Higher Order Multiagent Networks: An Attack Isolation-Based Approach

Current resilient consensus algorithms deal with multiagent networks with lower order nodal dynamics where each agent excludes certain extreme values from its neighbors. This does not scale well in general networks. In this article, a new type of resilient consensus algorithm based on distributed attack isolation (DAI-RC) is proposed for general higher order networks. In the DAI-RC algorithm, the evolution of each normal agent can avoid the influence from those neighbors which are isolated as victims of attack. To characterize a feasible communication topology to isolate attacked agents, a notion of <i>graph isolability</i> is proposed based on which a sufficient condition to isolate the attacked agents is presented. Simulations are finally provided to illustrate the effectiveness of the proposed algorithm.

On robust control of uncertain chaotic systems: a sliding-mode synthesis via chaotic optimization

This paper presents a novel Lyapunov-based control approach which utilizes a Lyapunov function of the nominal plant for robust tracking control of general multi-input uncertain nonlinear systems. The difficulty of constructing a control Lyapunov function is alleviated by means of predefining an optimal sliding mode. The conventional schemes for constructing sliding modes of nonlinear systems stipulate that the system of interest is canonical-transformable or feedback-linearizable. An innovative approach that exploits a chaotic optimizing algorithm is developed thereby obtaining the optimal sliding manifold for the control purpose. Simulations on the uncertain chaotic Chen’s system illustrate the effectiveness of the proposed approach.

Coordinated tracking in mean square for a multi-agent system with noise perturbations

In this paper, a coordinated tracking control problem for a multi-agent system under noise perturbations is considered over a leader-follower communication network. Two control gain functions are designed where the first one is used to attenuate the effect of noise and the second to stabilize the system. Using tools from the algebraic graph theory and stochastic analysis, it is proved that the followers can track the leader in mean square over a time-invariant network. The results are then extended to the scenario of a time-varying network.

Invulnerability of planar two-tree networks

Let us model the network by an undirected graph G, in which each edge fails independently with probability q ∈ [ 0 , 1 ] , the all-terminal reliability of the network is the probability that the graph G remains connected and it is one of the important measure for the invulnerability of the network. Clearly, the all-terminal reliability can be written as a polynomial in either q. Theoretically, it has been proved that calculating all-terminal reliability for planar networks is #P-complete. Up now we cannot find any results for some special classes of the planar networks. This paper studies the all-terminal reliability of the two-tree networks and its generalizations. A linear algorithm for calculating the reliability of a planar two-tree networks is proposed, with algorithmic complexity O ( n ) , where n is the number of steps. Then both the uniformly-most reliable network model and the uniformly-worst reliable network model are determined by using the algorithm. Finally, a polynomial algorithm for planar two-connected networks is proposed based on an expended algorithm and the corresponding uniformly-most reliable network model and uniformly-worst reliable network model are also presented, with computational complexity O ( n ) , where n is the number of steps.

Agreement dynamics of finite-memory language games on networks

No abstract is provided for this article.

Joint Coding/Decoding Optimization for DC-BICM System: Collaborative Design

Differential chaotic bit-interleaved coded modulation (DC-BICM) system can achieve coding gain from channel code without loss of bandwidth in the differential chaos shift keying (DCSK) system, but the current DC-BICM system using the belief propagation decoding algorithm has high decoding complexity, which brings burdens to resource-limited applications. In this letter, a novel collaborative design framework based on joint coding and decoding optimization is proposed for the DC-BICM system over multipath Rayleigh channels. Firstly, the column-weight-based (CWB) shuffled scheduling decoding is introduced into the DC-BICM system to lower the decoding complexity, called shuffled-based DC-BICM system. Then, a CWB extrinsic information transfer (CWB-EXIT) algorithm is developed for the theoretical analysis of this system. With the CWB-EXIT algorithm, a low-storage protograph low-density parity-check (P-LDPC) code is designed for this system, and the column-weight distribution is taken as an important constraint in the collaborative design process. In this way, the storage space used for storing the scheduling order in the CWB shuffled scheduling can be saved, whose size is proportional to code length. Theoretical analysis and simulations show that the shuffled-based DC-BICM system with the low-storage P-LDPC code can achieve lower decoding complexity, less storage requirement and better performance than the existing systems.

On a new hyperchaotic system

A new hyperchaotic system is presented, which has two large positive and one small negative Lyapunov exponent over a large range of parameters. As a consequence, system orbits strongly expand in some directions but rapidly shrink in some other directions. These strong expansions and shrinking lead the system orbits to be more disordered and random. Bifurcation and Poincaré-map analyses further show that the system has very rich bifurcations in different directions and extremely complicated dynamics overall. Spectral analysis shows that the system in the hyperchaotic mode has an extremely broad frequency bandwidth of high magnitudes, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.

Periodic orbits arising from Delta-modulated feedback control

A Delta-modulated feedback gives rise to a system of the form x+=f(x)=ax−Δ sgn(ax). In this paper, we will determine the a values, 1<|a|<2, for which periodic orbits of each order exist. Polynomials with “sign” coefficients are introduced, and their properties are investigated. With the help of the roots of these polynomials, we characterize the minimal value for |a| such that a periodic point of a certain order first appears. Our results show that even though the topological properties of the tent map and the map f are different, the mechanisms of giving rise to periodic orbits via parameter variations are exactly the same for −2<a<−1, and only “slightly” different for 1<a<2.

GaussianSource Coding Based on P-LDPC Code

A lossy source coding system based on the protograph low-density parity-check (P-LDPC) code is proposed for Gaussian source compression. In the proposed system, the conventional belief propagation (BP) algorithm is modified to be a concatenated BP-inverse BP (BP- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> BP) for encoding and decoding, where the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> BP is constructed by a fully-connected layer of a neural network. Compared to the existing approximate message passing algorithm, the proposed BP- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> BP realizes a float-to-bit compression with low complexity for arbitrary Gaussian sources. The BP- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> BP is implemented based on the linking relation of the protograph; therefore, it is necessary to optimally design the protograph to obtain better rate-distortion function (RDF) performance. Regarding the coding optimal procedure, a mutual information iteration convergence (MIIC) algorithm is designed as the optimal criterion to determine the source P-LDPC code with minimum distortion. Inspired by the plane construction of quantum stabilizer code, a lattice topological splicing (LTS) algorithm is proposed for regularly building the protograph to reduce the code searching complexity. By using the MIIC and the LTS algorithms, the BP- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> BP based on the designed P-LDPC code maintains good distortion performance close to the RDF limit.

Complex Canard Explosion in a Fractional-Order FitzHugh–Nagumo Model

This article investigates the complex phenomena of canard explosion with mixed-mode oscillations, observed from a fractional-order FitzHugh–Nagumo (FFHN) model. To rigorously analyze the dynamics of the FFHN model, a new mathematical notion, referred to as Hopf-like bifurcation (HLB), is introduced. HLB provides a precise definition for the change between a fixed point and an [Formula: see text]-asymptotically [Formula: see text]-periodic solution of the fractional-order dynamical system, as well as the stability of the FFHN model and the appearance of the HLB. The existence of canard oscillations in the neighborhoods of such HLB points are numerically investigated. Using a new algorithm, referred to as the global-local canard explosion search algorithm, the appearance of various patterns of solutions is revealed, with an increasing number of small-amplitude oscillations when two key parameters of the FFHN model are varied. The numbers of such oscillations versus the two parameters, respectively, are perfectly fitted using exponential functions. Finally, it is conjectured that chaos could occur in a two-dimensional fractional-order autonomous dynamical system, with the fractional order close to one. After all, the article demonstrates that the FFHN model is a very simple two-dimensional model with an incredible ability to present the complex dynamics of neurons.