2,312 publications from this institution
This paper characterizes some complex dynamics of Chen’s system. Some conditions of existence for pitchfork bifurcation and Hopf bifurcation are derived by using bifurcation theory and the center manifold theorem. Numerical simulation results not only show consistence with the theoretical analysis but also display some new and interesting dynamical behaviors including homoclinic bifurcation and the coexistence of two stable limit cycles and one chaotic attractor as well as some periodic solutions emerging from Hopf bifurcation but ending in homoclinic bifurcation, which are different from those reported in the literature before. All these show that Chen’s system has very rich nonlinear dynamics.
No abstract is provided for this article.
No abstract is provided for this article.
A constructive approach to the left coprime fractional representations for a class of (stable and unstable) nonlinear control systems described by certain multi-input/multi-output nonlinear ordinary differential equations is proposed. The method works for the coprimeness defined by Verma [15].
We propose yet another feedback control algorithm for chaotification of an originally non chaotic system. The new controller uses the continuous sawtooth function instead of the modulo operation, which can generate discrete chaos in the sense of Li and Yorke, for arbitrarily given nonlinear autonomous systems of any dimensionalities.
No abstract is provided for this article.
This Letter reports the finding of the compound structure of Chen's attractor, which is obtained by merging together two simple attractors after performing a mirror operation. Also, the forming procedure of Chen's attractor is explored.
This article introduces the notion of pinning control for complex dynamical networks regarding their stabilization, synchronization and control. Specifically, it will first review the concept of network pinning control and then address the fundamental issues of network stabilizability, synchronizability and controllability. Basic ideas will be explained, technical derivations will be outlined, and important theoretical problems will be briefly discussed. It will show that the self-contained theoretical framework of pinning control technology is promising for practical applications in network science and engineering.
With the deep integration of electric power and information technology systems, the distribution system shows the trend of increasingly complex structures and increasing external risk factors. This leads to more diversified types of faults in the distribution network, so it is crucial to optimize its topology. In this paper, we first compare the main connection modes of high-voltage and medium-voltage distribution networks in China, and combine them with the specific needs of Shaanxi Power Grid to propose a differentiated flexible network model and its scope of application. Using Graph Neural Network and Genetic Algorithm, an innovative optimization method of distribution network connection is proposed to support the typical network structure of the new distribution network. Analysis of examples shows that the proposed algorithm can improve the original network’s network loss and voltage deviation by 32.8% and 37.3%, respectively, and the improvement effect is better than that of the traditional genetic algorithm. At the same time, considering the different stages of distribution network development and the uncertainties that may be faced, this paper also explores the flexible transition scheme of each typical network structure to ensure a smooth transition to a more efficient, green and intelligent distribution network model without affecting the reliability of the existing power supply.
Topology identification of complex dynamical networks received extensive attention in the past decade. Most existing studies rely heavily on the linear independence condition (LIC). We find that a critical step in using this condition is not rigorous. Besides, it is difficult to verify this condition. Without regulating the original network, possible identification failure caused by network synchronization cannot be avoided. In this paper, we propose a new method to overcome these shortcomings. We add a regulation mechanism to the original network and construct an auxiliary network consisting of isolated nodes. Along with the outer synchronization between the regulated network and the auxiliary network, we show that the original network can be identified. Our method can avoid identification failure caused by network synchronization. Moreover, we show that there is no need to check the LIC. We finally provide some examples to demonstrate that our method is reliable and has good performances.
A general nonlinear model of disease spreading is proposed, describing the effect of the new link-adding probability p in the topological transition of the N-W small-world network model. The new nonlinear model covers both limiting cases of regular lattices and random networks, and presents a more flexible internal nonlinear interaction than a previous model. Hopf bifurcation is proved to exist during disease spreading in all typical cases of regular lattices, small-world networks, and random networks described by this model. It is shown that probability p not only determines the topological transition of the N-W small-world network model, but also dominates the stability of the local equilibria and bifurcating periodic solutions, and moreover can be further applied to stabilize a periodic spreading behaviour onto a stable equilibrium over the network.
Addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties. The Takagi-Sugeno (T-S) fuzzy model is adopted for fuzzy modeling of the nonlinear system. Two cases of the T-S fuzzy system with parametric uncertainties, both continuous-time and discrete-time cases are considered. In both continuous-time and discrete-time cases, sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability, for the T-S fuzzy system with parametric uncertainties. The sufficient conditions are formulated in the format of linear matrix inequalities. The T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic Lorenz system.
In this paper, we investigate some interesting properties of a scalar system controlled by Δ-modulated feedback. We show that there are three different cases. In the first case, there is a minimal global attractor which consists of only two points. The two points form either one 2-periodic orbit or two 1-periodic orbits (fixed points). We also characterize the attracting region for each of these two points. In the second case, the maximal stabilizable region is bounded, and there is a minimal local attractor inside this stabilizable region. In the third case, the maximal stabilizable set is a Cantor set, which is a repeller of the system, and the system is chaotic on the Cantor set.
This paper discusses a new design and implementation of a liquid mixing apparatus based on the commonly used stirred tank model. This mixer is capable of working under the control of different kinds of signals, including DC signals, periodic signals and chaotic signals. Chaotic signals, in particular, are generated and applied to the impeller/tank velocity control mechanism, exploring the efficacy of chaotic perturbations in liquid mixing. Comparable experiments reveal that the chaotic perturbations injected into the stirred tank help enhance the liquid mixing efficiency quite significantly, based on the sucrose dissolution experiments in our laboratory.
No abstract is provided for this article.
Combining the advantages of both integer-order and fractional-order complex chaotic systems, we propose a hybrid-order complex Lorenz system. We demonstrate its abundant chaotic characteristics, including symmetry and dissipation, fixed points and their stability and Lyapunov exponents, with 0-1 test. Then we show that, as the initial value, parameters and the order are varying, the system exhibits diverse dynamical behaviors, with fixed points, limit cycles and chaotic attractors. We further show that the system has coexisting attractors and parametric attractors. In addition, we find that the system generates different chaotic attractors as the system hybrid order varies, referred to as order attractors. Finally, we examine the dynamic transport of the hybrid-order complex Lorenz system and design a piecewise continuous controller to realize offset boosting control. By varying the initial value, parameters or orders, we realize the dynamic transport of the system. Our simulation results confirm the dynamic transport of the hybrid-order complex Lorenz system.
