Chaotic dynamics of oscillator based on lossless circuit

Equations that describe a new autooscillatory system with chaotic dynamics based on a lossless oscillatory circuit are presented. This system is capable of generating chaotic oscillations with irregular variations in the amplitude (amplitude chaos) at a small change in frequency. Bifurcation diagrams (one- and two-parametric), time series of the oscillatory process, and power spectra of the proposed system are presented.     

Controlled chaotic system with time delay

A chaotic autooscillatory system described by an equation with delayed argument is proposed, in which the oscillations are controlled by means of a chaotizing feedback algorithm. The results of numerical analysis of the proposed system are presented.     

Analysis of a controlled chaotic autooscillatory system based on an anharmonic oscillator model

The mathematical model of a new autooscillatory system with chaotic dynamics based on self-excitation of an anharmonic oscillator is considered. The results of numerical analysis show the possibility of generating chaotic oscillations with linear gain in the delayed feedback and controlling chaos by means of parametric self-action.     

Transition to phase synchronization in a system with periodic dynamics under the action of a chaotic signal

Intermittent behavior has been studied near the boundary of phase synchronization in an autooscillatory system with periodic dynamics under the action of an external chaotic signal. It is shown that the intermittency obeys the same scenario as that observed in the case of interaction between two coupled chaotic oscillators.     

Generalized synchronization in autooscillatory media

The phenomenon of generalized chaotic synchronization has been found in autooscillatory media described by the Ginzburg-Landau equations. A mechanism responsible for the establishment of generalized synchronization regimes in one-way coupled autooscillatory media exhibiting chaotic spatiotemporal behavior is proposed. The mechanism of generalized synchronization is described based on an analysis of a modified Ginzburg-Landau equation with an additional dissipative term.     

Information transmission using a synchronous chaotic response with filtering in the communication channel

A principle is proposed for obtaining a chaotic synchronous response in a driven nonlinear oscillatory system under conditions where the signal of the driving chaotic system is filtered by the coupling channel. Music and speech signals are used to demonstrate the efficiency of applying this principle to transmit information through a channel having a limited frequency band. Pis’ma Zh. Tekh. Fiz. 25, 71–77 (August 26, 1999)     

Generator of chaotic microwave oscillations based on a high-power bipolar transistor

A chaotic microwave autooscillatory system has been designed, implemented on a high-power bipolar transistor (2T 982 A-2), and studied. The experiments showed stable generation of chaotic oscillations in a 5.26?C5.44 GHz range with a spectral power density of 1.3 × 10^?3 W/MHz.     

Controlled oscillations in chain of unidirectionally coupled bistable oscillators with chaotic dynamics

Equations of a chain of n (n = 1, 2, ...) unidirectionally coupled bistable oscillators possessing chaotic dynamics are presented. Numerical analysis has been performed for a system of three identical autooscillatory systems with nonlinear elements admitting cubic approximation. It is shown that, as the degree of coupling between units in the chain increases, their motions in the phase space become more complicated and even chaotization of oscillations may take place at the parameters with which separate oscillators exhibit regular motions in the autonomous regimes. The features of the influence of a driving oscillator on the motions of a driven bistable subsystem are related to filtration of the driving signal in the circuit of the driven subsystem.     

Controlling attractor structure in bistable chaotic oscillator

The effect of the asymmetric characteristic of a nonlinear element in the Chua oscillator on the oscillatory process in this chaotic dynamical system has been studied. The system behavior was studied under the action of irregular oscillations modeling the intrinsic noise, rather than as excited by a single impact. It is established that a growth in the asymmetry parameter of the nonlinear element characteristic leads to an asymmetry of the chaotic attractor of the Chua oscillator that maps the switching of motions between the two basins of attraction. Then, the system exhibits a bifurcation, whereby chaotic oscillations arise in one of these basins and develop into motions that correspond to a multiple limit cycle.     

一类非线性振子中有界噪声诱发的混沌运动

研究谐和外力与有界噪声激励联合作用下的一类非线性振子的混沌运动。利用Melnikov方法，通过计算扰动系统的Melnikov积分，分析了系统在参数发生变化时的同宿分岔，得出系统产生混沌运动的参数阈值，并讨论了有界噪声激励对系统的混沌运动的影响。最后利用数值方法模拟了系统的安全盆的侵蚀状况，并进一步通过计算系统运动的Lyapunov指数，给出了由噪声诱发的混沌运动与噪声激励下非混沌运动之间的差别。     

Chaotic oscillator method: Approaches to diagnosing the parameters of nonlinear chaotic systems

The new method described is based on the use of nonlinear chaotic oscillatory systems. An analysis is made of the problem of choosing algorithms for estimating the parameters of nonlinear chaotic oscillatory systems from a measured signal. Deceased. Translated from Izmeritel'naya Tekhnika, No. 4, pp. 19–21, April, 2000.     

Features of induced synchronization of a bistable oscillator with chaotic dynamics

The features of induced synchronization of a Chua oscillator with a nonlinear element admitting cubic approximation have been numerically simulated for a system where the autonomous operation admits regular or chaotic regimes determined by losses in the oscillatory circuit. The cases of deterministic synchronization (under the action of a harmonic external driving signal) and chaotic synchronization (chaotic control) have been considered. It is established that, outside the band of synchronous oscillations that corresponds to the deterministic synchronization, the external harmonic signal stimulates the transformation of regular oscillations into chaos with the motions switched between two attractors. In cases of chaotic synchronization, there is a residual “noise” in the form of differential chaotic oscillations, which grows with increasing non-identity of the driving and driven signals.     

Intermittent generalized synchronization in distributed autooscillatory media described by complex Ginzburg-Landau equations

The appearance of an intermittent regime at the boundary of the generalized chaotic synchronization region has been found for distributed autooscillatory systems described by the complex Ginzburg-Landau equations, which occur in the regime of spatiotemporal chaos. The type of the observed intermittent generalized synchronization behavior is established.     

Dynamic chaos in the microwave range generated in SiGe-based autooscillatory structure

A chaotic microwave autooscillatory structure has been designed, implemented on a monolithic IC manufactured by 0.25-μm silicon-germanium technology, and studied. The experiments with the IC showed the possibility of generating stable chaotic oscillations in the 3–8-GHz range.     

Chaos in a bistable chain of two unidirectionally coupled autooscillatory systems with time delay

We have studied the dynamics of a chain of two unidirectionally coupled delay-feedback autooscillatory systems possessing smooth asymmetric amplitude characteristics and the initial conditions of opposite signs, which result in the formation of two basins of attraction in the chain. The results of numerical simulations of the process of chaotization in a driven autooscillatory system and the transition of its oscillations to a state of forced synchronization with a change in the basin of attraction are presented. The mechanism of chaotization is considered.     

Chaotic oscillations of two cascade-coupled oscillators with frequency control

The generation of chaotically modulated oscillations in autooscillatory systems with frequency control is considered. It is shown that, by coupling two such systems, it is possible to considerably expand a region corresponding to the generation of chaotic oscillations in the space of parameters of this ensemble and to provide additional means of controlling the characteristics of oscillations by changing the parameters of coupling.     

Self-synchronization of electrohydrodynamic autooscillations during multichannel discharges in electrolyte

The phenomenon of self-synchronization of electrohydrodynamic (EHD) autooscillatory processes during multichannel discharges in electrolyte was observed. The fundamental possibility of the synchronous generation of EHD autooscillations using a system of current concentrators was demonstrated by producing discharges in an aqueous sodium chloride solution using N = 2, 5, 32, and 56 current concentrators with a diameter of 0.2–0.5 mm and a relative size variance up to 0.37. The concentrators had the form of holes or metal electrodes in a dielectric plate. It is established that the mutual synchronization of EHD oscillatory processes in a system involving N current concentrators is ensured by an additional inductance in the discharge circuit. The process of self-induction accompanying current breakage by bubbles leads to the generation of overvoltage in the circuit, which provides synchronous discharge-breakdown initiation on the concentrators and ensures phase synchronization in the system.     

Reduced model of discrete‐time dynamic image segmentation system and its bifurcation analysis

We have developed a discrete‐time dynamic image segmentation system consisting of chaotic neurons and a global inhibitor. Our system receives an image with isolated regions and can output segmented images in time series based on oscillatory responses of chaotic neurons. In this article, we derive a reduced model to find intrinsic properties of the system of dynamic image segmentation. Using numerical method for analyzing dynamical systems, we investigated bifurcation phenomena of a fixed point observed in the reduced model. As the results, in a model of two coupled chaotic neurons, we found that a set of Neimark‐Sacker bifurcations causes the generation of an in‐phase oscillatory response, which is unsuitable for the purpose of dynamic image segmentation. The bifurcation analysis gives appropriate parameter values to exclude the generation of in‐phase oscillatory responses, i.e., our dynamic image segmentation system can work well. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 283–289, 2009     

Chaotic mixing in cross-channel micromixers

In this article we concentrate on a particular micromixer that exploits chaotic trajectories to achieve mixing. The micromixer we consider here is a cross-channel intersection, in which a main stream is perturbed by an oscillatory flow, driven by an external source. Depending on the amplitude and frequency of the oscillatory flow, one obtains wavy and chaotic regimes, reminiscent of a tendril-whorl mapping. The chaotic states, in which material lines are stretched and folded, favour mixing. A spatiotemporal resonance phenomenon, in which the material-line deformation is transient, is shown. An experiment using soft lithography and integrated valves, in which the resonant states are revealed, is described. From a practical viewpoint, the cross-channel micromixer offers a variety of regimes, which can be exploited to mix fluids or separate particles of different sizes. In the context of microsystems, it can be viewed as a 'smart' elementary system.     

非线性弹性直杆纵振时的混沌行为

研究了S形本构关系的弹性直杆纵振时的混沌行为.用Galerkin原理将杆纵振时的动力控制方程转化为二阶三次非线性微分动力系统;给出了其产生同宿轨道和异宿轨道的条件,得到了同宿轨道的参数方程;借助Melnikov函数给出了系统发生混沌的临界条件;数值计算给出了混沌运动区域随β和γ的变化规律,用分岔图、位移时程曲线、相平面图和Poincaré映射判断了系统的运动行为即定常还是混沌.进一步的研究还表明本构关系中的二次非线性项对系统的动力响应具有很大的影响.