Transformation of bistable chaotic oscillations in triggers of a ring system

Equations describing a ring system of three unidirectionally coupled Chua oscillators (subsystems) are presented. Numerical analysis is performed in the case in which only one subsystem is autooscillatory. It is shown that non-auto-oscillatory subsystems (simplified to single-shot trigger type) exhibit complication of circuit oscillations that is accompanied by multiplication of the oscillation frequencies and expansion of the generated spectrum.     

Chaotic synchronization in a system of inductively coupled oscillators

A system of two inductively coupled chaotic oscillators is considered. Normalized equations of motion for oscillators with arbitrary parameters are derived in the case of a cubic approximation of the nonlinear elements. The results of a numerical analysis of the features of interaction between chaotic coupled nonidentical subsystems are presented and a realistic experiment is described.     

Resonant oscillations of a weakly coupled, nonlinear layered system

Summary We analyze standing wave oscillations of a periodic system of infinite spatial extent composed of layers with cubic material nonlinearities that are coupled by weak linear stiffnesses. We show that nonlinear modal interactions in this system are unavoidable due to the existence of an infinite degenerate set of internal resonances. Considering only the dominant 13 resonances, the standing wave problem is formulated in terms of a bi-infinite set of coupled nonlinear difference equations that govern the layer modal amplitudes. In the limit of weak coupling between layers this set of difference equations is analyzed by (i) direct perturbation analysis, and (ii) matched asymptotic expansions of the differential equations resulting from a continuum approximation. Strongly and weakly localized, as well as spatially extended (non-localized) solutions are computed. In addition, composite solutions derived by matching in-phase and out of phase segments of the aforementioned solutions can also be constructed. In the limit of weak coupling between layers and/or strong material nonlinearities, the solutions develop sensitive dependence on initial conditions, and the possibility of spatial chaos in the system exists.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

Chaotic oscillations in mechanical systems

Chaotic oscillations have now been observed in non-linear mechanical systems by analytical, numerical and experimental methods. Nevertheless a more fundamental understanding of why and when such oscillations occur is of great importance. This goal will be pursued here by considering the relationship between chaos induced by forced oscillations versus self-excited oscillations, the relationship of indeterminancy of the final equilibrium state in the initial value problem to chaos in the sustained oscillation problem, comparison of theory to physical experiment, necessary and sufficient conditions for chaos to occur, and the question of convergence of systems of modal ordinary differential equations which derive from partial differential equations.     

Excitation of oscillations in a gas-blower-fluidized-bed system

It is shown that hydraulic characteristics in a fluidized bed oscillate in a spectrum that is discrete due to the reciprocal effect of the fluidization regime on gas-blower operation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 3, pp. 453–458, September, 1985.     

Synchronization of quasi-periodic oscillations in coupled phase oscillators

The phenomenon of synchronization of two oscillators under the action of an external force has been studied in a phase approximation. The Lyapunov maps are presented and the possible types of regimes are considered. Various types of two-frequency tori are revealed and classified.     

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-excited oscillations in a fiber-optic laser-collimator-microresonator system

This paper proposes and studies experimentally a design for a fiber-optic self-excited oscillator, characterized by high stability of the operating point. The design appears promising for developing fiber-optic transducers of physical quantities with a frequency output. Pis’ma Zh. Tekh. Fiz. 23, 33–39 (March 26, 1997)     

The use of coupled oscillations in piezoresonant sensor structures

The principles of the construction of piezoresonant sensor structures based on modulation of the parameters of coupled oscillations are considered. Examples of the construction of such sensors are are given. __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 59–61, March, 2006.     

Controlled stochastization of oscillations in a chaotic delayed-feedback system

A mathematical model of the ring autooscillatory system, which possesses chaotic dynamics and comprises a nonlinear amplifier with a differentiating element in the feedback chain, a nonlinear oscillatory circuit, and a delay line, is considered. Numerical analysis has been performed for irregularly varying initial conditions. These conditions were set by the solutions of equations describing chaos that simulated intrinsic noises of a real autooscillatory system. It is shown that the irregularly varying conditions of excitation can lead to stochastization of the chaotic oscillations, in which case the oscillatory process becomes irreproducible.     

弱耦合超晶格中的高频自维持振荡

研究了掺杂弱耦合ＧａＡｓ／ＡｌＡｓ超晶格在直流偏压作用下的电场畴及自维持振荡,分析了通过加光照,变温、加横向磁场等方法使稳定场畴向动态场畴转换并产生自维持振荡的机制备指出有效漂移速度Ｖ（Ｂ,Ｆ）曲线线形对纵向输动行为的重要影响。在ＧａＡｓ／ＡｌＡｓ窄势垒超晶格中得到了室温下千兆赫微波振荡。     

Transient chaotic oscillations of a tethered satellite system

Summary For the simulation of large amplitude motions of thin, visco-elastic tethers connecting two satellites several numerical algorithms were developed recently. However, since we are dealing with highly nonlinear, nearly Hamiltonian multiple degree of freedom systems we typically will have to expect transient chaotic motions if the motion starts in the neighborhood of a saddle point. For tethered satellite systems we have two stable radial and two unstable tangent-to-orbit equilibria. By simulation with a specially adapted finite-element program we show that the asymptotic behaviour of the system strongly depends on the choice of the initial conditions. Thus, starting in the vicinity of an unstable equilibrium, we cannot predict in which of the attractors it settles down finally. A simple tether model by V. Beletsky and D. Pankova is used to demonstrate the fractal nature of the basin boundary of the two attractors.     

Excitation and suppression of oscillations in a chain of unidirectionally coupled elements with neuron-like dynamics

The propagation of pulses in a model chain of Hindmarsh-Rose neurons with unidirectional coupling has been studied in the presence of intrinsic dynamics in chain elements. The main regimes of oscillations in the model chain are determined as dependent on the coupling parameter. The mechanisms of activation and suppression of oscillations in the model chain under the action of rectangular pulses are explained using the results of a detailed analysis of the basins of attraction of a stable immobile point and a periodic attractor of a model neuron.     

The time of synchronization of oscillations in two coupled identical subsystems

The mechanism of synchronization of oscillations in two identical coupled flow systems has been studied. The time (past the coupling onset) during which a synchronous oscillation regime is established depends on the oscillation phase difference between the subsystems. Variation of the coupling parameter leads to a change in the character of dependence of the synchronization time on the phase difference. Several types of synchronization processes are revealed, which are realized for various values of the coupling parameter.     

Near-resonance oscillations of a nonsymmetric nonlinear system with a crack

The Malkin method, which was developed to construct a single unique resonance solution of nonlinear equations, is generalized for the case of the derivation of all stationary solutions in the near-resonance zone, and also for transient oscillations.Kiev Polytechnic Institute. Translated from Problemy Prochnosti, No. 10, pp. 108–112, October, 1989.     

Thermohydraulic oscillations in a system showing natural circulation of a two-phase coolant

Thermohydraulic oscillations are considered for a wide range in coolant thermophysical parameters.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 3, pp. 419–425, March, 1990.     

Modelling and analysis of coupled nonlinear oscillations of a floating body in two degrees of freedom

Summary We describe a mathematical model to investigate the effect of coupled nonlinear oscillations of a floating body in time domain under the influence of sinusoidal waves. To account for hydrodynamic forces, a mathematical formulation for added mass moments of inertia, damping and restoring moments is presented for roll and yaw. Using perturbation technique, we obtain order wise solutions in the normalized domain wherein the assumption on small distortion holds. On applying Laplace transform, a zeroth-order solution is obtained in closed form whereas for higher order solutions we resort to the Runge-Kutta method with adaptive step size algorithm. For analyzing the model result we perform numerical experiments for a vessel of mass 19190 tons under the action of a beam wave of frequency 0.74 rad/sec and 1.0 m wave height. The validity of the numerical scheme is checked by comparing with the analytical solution for uncoupled zeroth-order roll and then we proceed to examine the effect of coupled behavior of roll and yaw for higher-order approximations. The inter-dependence between wave frequency (ω), system frequency (β) and damping factor (ζ) is obtained to reveal system stability. Model results indicate an artificial increase in amplitude for uncoupled roll, and also emphasize the contribution of viscous damping in roll in contrast to added mass in yaw.     

弦-梁耦合系统的动力学行为分析

本文研究了弦-梁耦合系统在初始平衡解处的稳定性与分岔情况,给出了特征值随阻尼参数的变化情况,并利用稳定性分析和特征值分析等解析方法,得到了初始平衡解、周期解和拟周期解的稳定边界以及导致Hopf分岔和2维胎面等分岔解的临界分岔曲线。最后,利用数值模拟方法研究了弦-梁耦合系统的稳定性与分岔情况。     

Electromagnetically-induced transparency in a multi-cavity coupled waveguide system

The plasmonic analogue of electromagnetically-induced transparency (EIT) was investigated in a plasmonic waveguide system composed of a straight waveguide, with rectangular and U-shaped (split-ring resonator) cavities. An EIT-like transparency window occurs in the transmitting spectrum of the waveguide system and the magnetic field is dramatically changed due to the destructive interference between two resonance pathways. It is demonstrated that the EIT-like spectra can be modified by varying the coupling strength and tailoring the degree of asymmetry of the structure, and we study the coupling mechanisms between the elements of the structure, including magnetic coupling, electric coupling, and inductive coupling. In addition, a cascaded structure which consists of an SRR pair with 180° rotation asymmetry has been studied. It is found that the strong couplings between two asymmetric plasmonic nanostructures can lead to EIT-like transmission in both visible and near-infrared regions, simultaneously.     

Controlled oscillations in an autostochastic system

Processes in a nonautonomous autostochastic system possessing an attractor of the Chen type were analyzed by numerical methods. The system was described by a set of equations for coupled oscillators with inertia. It is demonstrated that autooscillations can be controlled when a regular signal acts unidirectionally upon chaotic oscillations or, vice versa, when chaotic oscillations act upon the regular ones.