We study the stochastically forced Chen system in its parameter zone under the transition to chaos via period-doubling bifurcations. We suggest a stochastic sensitivity function technique for the analysis of stochastic cycles. We show that this approach allows to construct the dispersion ellipses of random trajectories for any Poincaré sections, and these ellipses reflect the essential features of a spatial arrangement of random trajectories near deterministic cycles. For the Chen system, we demonstrate a growth of stochastic sensitivity of the forced cycles under transition to chaos.
A class of planar diffeomorphims is formulated, with infinitely many coexisting Smale horseshoes, where the Lebesgue measure of the parameters with such strange dynamics is infinite. On each horseshoe, there exists a uniformly hyperbolic invariant set, on which the map is topologically conjugate to the two-sided full-shift on two symbols. Moreover, the topological entropy is infinite in certain parameter regions.
By geometric analysis, we discuss the riddled property of the basin of attraction of the Chen attractor based on Milnor’s definition, and prove that any neighborhood of the Chen attractor contains repelled sets with positive Lebesque measures. Our analytic and numerical results show that the Chen attractor indeed has some unusual properties leading to a “strange attractor” in the sense of Milnor.
Our interest in this paper is to design and apply the simplest possible artificial neural networks for identifying and controlling chaotic systems. To illustrate the effectiveness of these NN controllers, we show some convincing computer simulations in the identification and control of the chaotic Duffing oscillator and chaotic cellular neural networks.
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, a new filtering problem for sensor networks is investigated. A new type of distributed consensus filters is designed, where each sensor can communicate with the neighboring sensors, and filtering can be performed in a distributed way. In the pinning control approach, only a small fraction of sensors need to measure the target information, with which the whole network can be controlled. Furthermore, pinning observers are designed in the case that the sensor can only observe partial target information. Simulation results are given to verify the designed distributed consensus filters. </para>
This brief presents the first observations of multivaluedness in four systems: a random process, a nonlinear nondynamical system, a nonlinear dynamical system with nonlinearly sensed input and output and an adaptive linear estimator. The preliminary findings reported here suggest the impact of multivaluedness in different types of networks to range from adverse to benign or even essential.
Cardiac arrhythmias have been closely linked to a variety of dynamic bifurcations such as Hopf bifurcation and period doubling bifurcation. This paper describes the utility of bifurcation control for suppressing pathological rhythms (such as cardiac alternans) in nonlinear models of cardiac electro-physiologic activities. Bifurcation control methods that deal with Hopf bifurcation and border-collision bifurcation are employed. Washout filter aided feedback controllers are designed to control the location and stability of the bifurcations, as well as the amplitude of the bifurcated solutions. Important features of the dynamic control laws include equilibrium preservation even in the presence of model uncertainty, and automatic targeting of the orbits to be controlled. An independent experiment of suppressing cardiac alternans in a piece of dissected rabbit heart demonstrates the viability and utility of the proposed bifurcation control approach. Controlling nonlinear cardiac dynamics may have important clinical implications because arrhythmias in the heart such as fibrillation and ectopic foci are life threatening. The controller designs described here can lead to the development of future smart clinical pacemakers.
The transition from regularity to chaos in the sense of Li–Yorke is investigated in this Letter. A logistic network is investigated in detail, where all nodes in the network are the same logistic maps in non-chaotic states (with the parameter μ in non-chaotic regions). It is proved that when μ > 1 , these non-chaotic logistic nodes can become chaotic in the sense of Li–Yorke. Extensive simulations lead to the conjecture that when μ ⩽ 1 such a logistic network is “super-stable”, because no matter how strong the coupling strength is, the network does not transfer to a chaotic state.
This Letter introduces some new chaotic attractors in striped rectangular shapes. The chaotic attractors are constructed by adding bounded and non-smooth feedback control to the Rössler system. The shape of a generated chaotic attractor can be adjusted by changing some control parameters. Moreover, the dynamical behavior of the considered system is investigated and some estimations for characteristics of this attractor are given.
Herein, we prepared dual-stabilizer-capped CuInZnS/ZnS (CIZS/ZnS) quantum dots (QDs) in aqueous media via hydrothermal routes. On using the combination of poly (styrenesulfonic acid-co maleic acid) and glutathione stabilizers, we found that dual stabilizers effectively coat the surface of CIZS/ZnS QDs, resulting in high quantum yields and carboxylic acid groups that conjugate with various materials. To demonstrate their potential biomedical application, the dual-stabilizer-capped CIZS/ZnS QDs were conjugated with 3-aminophenylboronic acid, termed CIZS/ZnS@APBA, for HeLa tumor cell labeling. In vitro and in vivo assessments using HeLa cells and zebrafish embryos, respectively, revealed that these CIZS/ZnS@APBA nanoprobes exhibit low cytotoxicity under our experimental conditions. Confocal scanning laser imaging demonstrated that the nanoprobes can be efficiently internalized and are localized in the cytoplasm of HeLa cells. This work reveals the potential for use of CIZS/ZnS@APBA as a safe and effective targeted probe for in vivo imaging of cancer.
This paper studies feedback control of limit cycle amplitudes in nonlinear systems. A suitable implementation of the design is developed via an approximation of the time-derivative term in the nonlinear state feedback controller. A classical model is finally simulated for illustration of the proposed control method.
