2,312 publications from this institution
An equivalent relationship between the generalized ergodicity, almost everywhere E-chain transitivity, and the domain of influence of an invariant set for a discrete dynamical system on a compact metric space is explored. A necessary and sufficient condition for an invariant set to be a periodic orbit is given
One key factor affecting the distributed Nash equilibrium (NE) seeking in aggregative games is the unbalanced communication structure for multiple players. Although some results on seeking NE over undirected or weight-balanced graphs were established, how to address the distributed NE seeking problem over general directed communication graphs is still an outstanding challenge. This paper addresses the NE seeking problem for a class of aggregative games with general directed communication graphs. To achieve this objective, two new kinds of distributed discrete-time NE seeking algorithms are developed for aggregative games over fixed digraphs and time-varying digraphs, respectively. In particular, motivated by the heavy-ball method in optimization studies, a momentum term is introduced to the update law of the players' actions and it is numerically verified that this momentum term accelerates the convergence of the proposed algorithms. For both strongly connected fixed graph and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$B$ </tex-math></inline-formula> -strongly connected time-varying graph, it is theoretically proved that the actions of players will converge to the NE of aggregative games for the case of decreasing step-size implemented by the proposed NE seeking algorithms if the cost functions and the aggregation of players satisfy some certain conditions. Finally, the developed NE seeking algorithms are applied to the energy consumption control of plug-in hybrid electric vehicles (PHEVs), which demonstrates the effectiveness of the theoretical results.
No abstract is provided for this article.
It is important to present global non-linearized approximate method when the studies of nonlinear dynamical systems have been entering dominated fields.Seven different non-linearized approximate systems were given for a class of typical Hamiltonian system according to the different cases of two or three interaction points of equating potential lines.The approximate solutions(orbits)were given by integrating the corresponding approximate systems.It shows that the approximate elliptic periodic orbits can be obtained by the corresponding linearized systems and that the homoclinic(or heteroclinic) orbits can be obtained by the corresponding non-linearized systems with two or three order nonlinearities.Finally,the approximate methods are applied to analyze a concrete Hamiltonian system.
In this paper, discretization behaviors of sliding mode control (SMC) systems with matched uncertainties are studied. Some inherent dynamical properties of discretized second-order systems are explored. Upper bounds for system steady states are established. The analysis for the second-order systems is then extended to higher-order systems. Simulations are presented to verify the theoretical results.
In this work, a flexible triboelectric nanogenerator (TENG) consisting of a flexible printed circuit and microcavity surface polydimethylsiloxane (PDMS) for harvesting power was proposed and studied. The electric power generated from the TENG is based on the triboelectric effect and electrostatic induction. The cavity surface demolded from the sandpaper was employed for improving the TENG performance. The TENG could be operated in the vertical contact mode and bending contact mode. In order to estimate the performance in the different motion modes, two measurement setups were designed for measuring the TENG output power. According to the measurement results, higher cavity density has better output performance. The maximum output power of 1.77 μW with the 6.55 MΩ loading resistance for the vertical contact mode and the maximum output power 0.38 μW with the 6.95 MΩ loading resistance for the bending contact was achieved, respectively.
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.
This Letter introduces a new method—mode decomposition—for stability analysis of periodic orbits. Using this method, the stability of a periodic solution of an autonomous system, as well as the stability of synchronization within three chaotic systems with linear coupling, can be analyzed. As an example, a rigorous sufficient condition on the coupling coefficients for achieving chaos synchronization is obtained, for the case of three-coupled identical Lorenz systems. Numerical simulations are shown for demonstration.
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this brief, a new scheme is developed for chaos control by applying periodic impulsive parametric perturbations. Based on Melnikov's condition for the existence of chaos, it is mathematically proven that, in a neighborhood of a homoclinic orbit of the Duffing system, chaos can be suppressed. A sufficient condition is also established, serving as the design criterion for the amplitude and the width of the impulsive control signal. Finally, the control effect will clearly be demonstrated with simulation results. </para>
Extended Kalman filters - standard, modified and ideal, M.J. Moorman and T.E. Bullock bias in extended Kalman filters - a mathematical analysis, T.E. Bullock and M.J. Moorman robust adaptive Kalman filtering, A.R. Moghaddamjoo and R.L. Kirlin on-line estimation of signal and noise parameters and adaptive Kalman filtering, P.J. Wojcik adaptive Kalman filtering under irregular environment, G. Chen fisher initialization in the presence of ill-conditioned measurements, D. Catlin initializing the Kalman filter with incompletely specified initial conditions, A. Maravall and V. Gomez set-valued Kalman filtering, D. Morrell and W.C. Stirling distributed filtering using set models for systems with non-Gaussian noise, L. Hong suboptimal Kalman filtering for linear systems with non-Gaussian noises, H.Y. Wu and G. Chen robust stability analysis of Kalman filter under parametric and noise uncertainties, B.S. Chen numerical approximations and other structural issues in practical implementations of Kalman filtering, T.H. Kerr.
No abstract is provided for this article.
We investigate the dynamics of phase locking in a minimal neuronal network, which is composed of two Morris–Lecar neurons that are coupled by inhibitory and excitatory synapses as the synaptic strength is varied. Studies show that the synaptic strength can induce various phase locking modes and complex chaotic behaviors. In particular, two coupled neurons may display the complicated transitions between various periodic phase locking modes and chaotic states. It is shown that those transitions are accompanied by the tangent bifurcation, where the different phase locking modes can be related to the appearance of periodic windows. Furthermore, we explore the dynamical mechanism of the phase locking modes by means of the phase plane analysis. Interestingly, we have found two types of 2:1 phase locking modes, which are characterized by a thin tadpole tail and a fat tadpole tail, respectively. And then, two types of 2:1 phase locking modes are analyzed in detail for understanding their dynamical mechanism. The obtained results can be helpful to explore realistic neuronal activities.
This is an Editorial. It is amazing and also exciting to see a new journal Chaos Theory and Applications established recently. After chaos was coined with a precise model, the Lorenz system, more than half a century ago, there have already been many well-known journals on chaos such as, to name just a few specialized ones, Chaos, Chaos Solitons and Fractals, International Journal of Bifurcation and Chaos, Nonlinear Dynamics, and several Physical Review journals. Therefore, on the one hand, organizing a new journal on chaos needs a lot of courage and planning, and on the other hand, one can see that the chaos is still an ever-young subject for scientific research today. It is our expectation, therefore, that the new journal Chaos Theory and Applications could contribute more to this new direction of chaos research, along with other traditional topics.
Predictive fuzzy PID control theory is developed in this paper, which offers a new approach for robust control of time-delay systems. The paper describes the functional structure, design principle, and stability analysis of a new predictive fuzzy PID controller. Sufficient computer simulations are provided for illustration and verification. First, the structure of the controller is derived from both the fuzzy PID control and the generalized predictive control concepts. Then, on-line model identification, optimal cost index, fuzzification, rule base, and defuzzification of the representative predictive fuzzy PD+I controller are discussed in detail. Lyapunov asymptotic stability analysis is conducted. Then, many computer simulations are performed to compare with several closely related controllers such as the fuzzy PD+I controller and the Smith-type predictive fuzzy PD+I controller. In the simulations, second-order linear systems with/without time delays, nonlinear systems with/without time delays, uncertain linear systems with time delays, and uncertain nonlinear systems with time delays are used to confirm the advantages of the new predictive fuzzy PD+I controller. Finally, this method is applied to control some chaotic systems with success. This predictive fuzzy control method provides a new way for controlling uncertainty and complex linear and nonlinear systems, even with significant time delay.
