2,312 publications from this institution
A frequency-analytic methodology for controlling the amplitudes and stability of Neimark-Sacker bifurcations exhibited by discrete-time systems is presented. The proposed controller consists of a nonlinear static feedback law and a highpass filter used to preserve the dynamical behaviors of the system's equilibria. A simple example is included to illustrate the application of the method.
A three-dimensional continuous autonomous chaotic system with a 4-scroll attractor was recently reported and studied. In this paper, we further investigate the control and synchronization of this chaotic system. By simply adding and adjusting a constant control term, considered as the "controller," the chaotic system can display complex dynamics, with a different form of a 4-scroll attractor in a compound structure. In addition, synchronization between two such chaotic attractors is achieved and realized by both simulation and circuitry.
This paper is concerned with a leader-follower problem for a multi-agent system with a switching interconnection topology. Distributed observers are designed for the second-order follower-agents, under the common assumption that the velocity of the active leader cannot be measured in real time. Some dynamic neighbor-based rules, consisting of distributed controllers and observers for the autonomous agents, are developed to keep updating the information of the leader. With the help of an explicitly constructed common Lyapunov function (CLF), it is proved that each agent can follow the active leader. Moreover, the tracking error is estimated even in a noisy environment. Finally, a numerical example is given for illustration.
No abstract is provided for this article.
No abstract is provided for this article.
An elliptic partial differential operator satisfies the Gårding inequality, which leads to a Fredholm operator when the boundary conditions are also properly posed. In many applications, this Fredholm operator has zero index. Therefore n orthogonality (or, compatibility) conditions must be satisfied by the data, and the solutions have n degrees of freedom-they are nonunique. In order to fix those n degrees of freedom for the uniqueness of the solution, n accessory linear conditions are usually prescribed. This leads to an augmented system. In this paper, we formulate a simple operator-theoretic theorem to enable us to characterize when the augmented linear system is uniquely solvable. We apply this theorem to the Neumann problem as well as to the traction boundary value problem in elastostatics based upon a simple layer potential boundary integral approach. Criteria of unique solvability are established for several types of accessory conditions for such boundary value problems.
In this paper, we develop and apply some digital design and redesign techniques for ordering the chaotic Chua's circuit. The idea of using sampled-data feedback for controlling the circuit was previously suggested [Yang & Chua, 1998], which relies on small sampling periods. We show how this sampled-data feedback control method can be significantly improved, so that large sampling times are allowed, for the same purpose of ordering the nonlinear circuit, from anywhere within the chaotic attractor towards a predesired periodic cycle of the circuit.
Minimal edge controllability of directed networks is investigated in this paper. A new edge dynamics model is first introduced with two nonzero parameters describing the linear relationship between the node states and the edge states. Three different digraphs as skeleton structures for minimal edge controllability are analyzed. The conditions ensuring both node controllability and edge controllability for these three digraphs are presented, respectively. It is found that cycles in these networks play an important role in edge controllability. The notion of minimal edge controllability is then extended to signed digraphs. It is shown that the minimal edge controllability of a signed cycle depends on the number of edges with negative weights, regardless of the placement of the negative weights on the edges. Some examples are presented for illustration and verification.
In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.
This paper studies the following nonlinear two-dimensional partial difference system: Δ1(xmn−bmng(ymn)=0, T(Δ1Δ2)(ymn+amnf(xmn)=0, where m, n ϵ N i = {i, i + 1,…}, i is a nonnegative integer, T(Δ 1, Δ 2) = Δ 1 + Δ 2 + I, Δ 1 y mn = y m+1,n − y mn , Δ 2 y mn = y m,n+1 − y mn , I mn y mn = Y mn , {a mn } and {b mn } are real sequences, m, n ϵ N 0, and f, g : R → R are continuous with of uf(u) > 0 and ug(u) > 0 for all u ≠ 0. A solution ({x mn }, {y mn }) of this system is oscillatory if both components are oscillatory. Some sufficient conditions are derived for all solutions of this system to be oscillatory.
No abstract is provided for this article.
We study geographical effects on the spread of diseases in lattice-embedded scale-free networks. The geographical structure is represented by the connecting probability of two nodes that is related to the Euclidean distance between them in the lattice. By studying the standard susceptible-infected model, we found that the geographical structure has great influences on the temporal behavior of epidemic outbreaks and the propagation in the underlying network: the more geographically constrained the network is, the more smoothly the epidemic spreads, which is different from the clearly hierarchical dynamics that the infection pervades the networks in a progressive cascade across smaller-degree classes in Barabási–Albert scale-free networks.
