2,312 publications from this institution
The problem of making a stable linear time-invariant (LTI) system chaotic by using state-feedback control of arbitrarily small magnitude is studied. The feedback controller used is a simple sawtooth or modulo function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, thereby yielding chaotic dynamics. In fact, we mathematically prove that this controlled system is chaotic in the sense of Li and Yorke (1975).
We describe the emergence of complex cardiac rhythms in a nonlinear model of the atrioventricular (AV) nodal conduction system, and a method based on linear time-delay feedback (LTDF) control for suppressing them. The LTDF controller is effective at suppressing these rhythms by stabilizing the map to one of a set of unstable fixed points. Additionally, we show that the method is robust to both measurement error and experimental noise.
To find the exact explicit solution of the concatenation model, the corresponding differential system of the amplitude component is used, which is a planar dynamical system with a singular straight line. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by Li and Chen [2007], its corresponding traveling wave system is solved and analyzed, obtaining the corresponding phase portraits and showing the dynamical behavior of the amplitude component. Under different parameter conditions, exact explicit solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions, compacton solutions, as well as peakons and periodic peakons, are found explicitly.
In this report, by the numerical continuation method, we visualize and connect hidden chaotic sets in the Glukhovsky–Dolzhansky, Lorenz and Rabinovich systems using a certain path in the parameter space of a Lorenz-like system.
The consensus problem for multi-agent systems with general linear node dynamics and a fixed directed topology is investigated in this paper. Unlike existing linear multi-agent system models, the information transmission between neighboring agents are assumed to be intermittent in the present framework. To achieve consensus, a new class of distributed protocols are designed. By using tools from matrix analysis and switching systems theory, it is shown that this consensus problem can be cast to the stability problem of a set of low-dimensional switching systems. It is then proved that there exists a protocol guaranteeing consensus if the communication rate is larger than a threshold value and the communication topology contains a directed spanning tree. At last, a multi-step intermittent consensus protocol design procedure is provided for constructing such a protocol.
In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution and node betweenness centrality, but have very different synchronizabilities. This demonstrates the complexity of the network synchronizability problem. For a given network with identical node dynamics, it is further shown that two key factors influencing the network synchronizability are the network inner linking matrix and the eigenvalues of the network topological matrix. Several examples are then provided to show that adding new edges to a network can either increase or decrease the network synchronizability. In searching for conditions under which the network synchronizability may be increased by adding edges, it is found that for networks with disconnected complementary graphs, adding edges never decreases their synchronizability. This implies that better understanding and careful manipulation of the complementary graphs are important and useful for enhancing the network synchronizability. Moreover, it is found that an unbounded synchronized region is always easier to analyze than a bounded synchronized region. Therefore, to effectively enhance the network synchronizability, a design method is finally presented for the inner linking matrix of rank 1 such that the resultant network has an unbounded synchronized region, for the case where the synchronous state is an equilibrium point of the network.
For neural networks with constant or time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are studied in this paper. An approach combining the Lyapunov–Krasovskii functionals with the linear matrix inequality is taken to investigate the problems, which provide bounds on the interconnection matrix and the activation functions, so as to guarantee the systems' exponential stability. Some criteria for the exponentially stability, which give information on the delay-dependence property, are derived. The results obtained in this paper provide one more set of easily verified guidelines for determining the exponentially stability of delayed neural networks, which are less conservative and less restrictive than the ones reported so far in the literature.
A new one-way hash function based on the unified chaotic system is constructed. With different values of a key parameter, the unified chaotic system represents different chaotic systems, based on which the one-way hash function algorithm is constructed with three round operations and an initial vector on an input message. In each round operation, the parameters are processed by three different chaotic systems generated from the unified chaotic system. Feed-forwards are used at the end of each round operation and at the end of each element of the message processing. Meanwhile, in each round operation, parameter-exchanging operations are implemented. Then, the hash value of length 160 bits is obtained from the last six parameters. Simulation and analysis both demonstrate that the algorithm has great flexibility, satisfactory hash performance, weak collision property, and high security.
In this paper, the complex dynamical behaviors of the chaotic trajectories of Chen's system are analyzed in detail, with its precise bound derived for the first time. In particular, it is rigorously proved that all nontrivial trajectories of the system always travel alternatively through two specific Poincaré projections for infinitely many times. The results provide an insightful understanding of the complex topological structure of Chen's chaotic attractor.
No abstract is provided for this article.
We apply the Timoshenko theory to investigate a new mathematical modeling problem for the "shoulder-elbow-like" single flexible-link robot arms damping. Detailed analysis and derivation are given to support the mathematical modeling of this particular flexible mechanism. Moreover, by assuming that the pinned-pinned mode shape of a Euler-Bernoulli beam is the same as the more complete Timoshenko beam, an analytic solution of the new model is derived. Finally, computer simulation results are included to verify the theoretical analysis and mathematical formulation, which have shown satisfactory agreement with the new mathematical model.
This article addresses the H 2 norm accumulation problem of linearly coupled dynamical networks. An interesting outer-coupling relationship is constructed, under which the H 2 norm of the newly constructed network with column-input and row-output matrices increases exponentially fast in terms of the node number N: it increases generally much faster than 2 N when N is large while the H 2 norm of each node is 1. However, the H 2 norm of the network with a diffusive coupling is equal to γ2 N, i.e. increasing only linearly, when the network is stable, where γ2 is the H 2 norm of a single node. And the H 2 norm of the network with antisymmetrical coupling also increases, but rather slowly, with respect to the node number N. Other networks with block-diagonal-input and block-diagonal-output matrices behave similarly. It demonstrates that the changes of H 2 norms in different networks are very complicated, despite the fact that the network structures are linear. Finally, the influence of the H 2 norm of the locally linearised network on the output of a network with Lur'e node dynamics is discussed, demonstrating a significant effect of the H 2 norm on the network output synchronisation behaviours.
<p>We present a direct solution to the problem of constructing a stochastic matrix with prescribed eigenspectrum, widely referred to as the stochastic inverse eigenvalue problem. The solution uses Markov state disaggregation to construct a Markov chain with stochastic transition matrix possessing the required eigenspectrum. Existing solutions that follow the same approach are limited to constructing matrices with real-valued eigenspectra only. The novel solution directly constructs matrices with complex-valued eigenspectra by applying a new disaggregation technique in tandem with a technique from a previous solution. Due to this generalization, the novel solution is able to successfully model physical systems from a larger family. Furthermore, the novel solution constructs the matrix in a finite and predetermined number of iterations, and without numerical approximation. The solution is demonstrated by deriving an expression for a set of 4 x 4 stochastic matrices sharing the same prescribed complex-valued eigenspectrum and indexed by a real parameter.</p>
No abstract is provided for this article.
A very large infinite-dimensional Banach space of bounded nonlinear operators is suggested as an underlying framework for studies of nonlinear systems control. Meanwhile, it is pointed out that all results obtained in Verma [6] can be extended to this much larger family of nonlinear control systems.
This paper proposes a methodology for stabilization of nonlinear discrete-time systems exhibiting bifurcation phenomena under input constraints. The new stabilizing control law is a combination of a bounded feedback chaotification law and a bounded local stabilization law. The proposed control scheme is applied to the control of pathological rhythm in a cardiac model that undergoes a period-doubling bifurcation into alternans.
