Regular nonlinear response of the driven Duffng oscillator to chaotic time series

Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated.

Dynamical characteristics of an HP memristor based on an equivalent circuit model in a chaotic oscillator

To develop real world memristor application circuits, an equivalent circuit model which imitates memductance （mem- ory conductance） of the HP memristor is presented. The equivalent circuit can be used for breadboard experiments for various application circuit designs of memristor. Based on memductance of the realistic HP memristor and Chua＇s circuit a new chaotic oscillator is designed. Some basic dynamical behaviors of the oscillator, including equilibrium set, Lyapunov exponent spectrum, and bifurcations with various circuit parameters are investigated theoretically and numerically. To con- firm the correction of the proposed oscillator an analog circuit is designed using the proposed equivalent circuit model of an HP memristor, and the circuit simulations and the experimental results are given.

Experimental observation of partial amplitude death in coupled chaotic oscillators

The dynamics of coupled Lorenz circuits is investigated experimentally. The partial amplitude death reported in Phys. Rev. E 72, 057201（2005） is verified by physical experiments with electronic circuits. With the increase of coupling constant, the coupled circuits undergo the transition from the breakdown of both the reflection symmetry and the translational symmetry to the partial amplitude death. Its stability is also confirmed by analysing the effects of noise.

Explosive synchronization of complex networks with different chaotic oscillators

Recent studies have shown that explosive synchronization transitions can be observed in networks of phase oscillators [Goemez-Gardenes J, Goemez S, Arenas A and Moreno Y 2011 Phys. Rev. Lett. 106 128701] and chaotic oscillators [Leyva I, Sevilla-Escoboza R, Buldu J M, Sendifia-Nadal I, Goemez-Gardefies J, Arenas A, Moreno Y, Goemez S, Jaimes-Reaitegui R and Boccaletti S 2012 Phys. Rev. Lett. 108 168702]. Here, we study the effect of different chaotic dynamics on the synchronization transitions in small world networks and scale free networks. The continuous transition is discovered for R6ssler systems in both of the above complex networks. However, explosive transitions take place for the coupled Lorenz systems, and the main reason is the abrupt change of dynamics before achieving complete synchronization. Our results show that the explosive synchronization transitions are accompanied by the change of system dynamics.

Hydrodynamic simulation of chaotic dynamics in InGaAs oscillator in terahertz region

Hydrodynamic calculations of the chaotic behaviors in n^+nn^+In0.53Ga0.47As devices biased in terahertz(THz)electric field have been carried out.Their different transport characteristics have been carefully investigated by tuning the n-region parameters and the applied ac radiation.The oscillatory mode is found to transit between synchronization and chaos,as verified by the first return map.The transitions result from the mixture of the dc induced oscillation and the one driven by the ac radiation.Our findings will give further and thorough understanding of electron transport in In0.53Ga0.47As terahertz oscillator,which is a promising solid-state THz source.

Bifurcation Analysis of the Voltage Controlled Photosensitive Chaotic Oscillator

A photosensitive chaotic oscillator which can be controlled with light illumination under various control voltage levels is proposed.The oscillator consists of a photodiode for the light input,clock switches and capacitors for the sample and hold function,a nonlinear function that creates an adjustable chaos map,and a voltage shifter that adjusts the output voltage for feedback.After optimizing the photodiode sub-circuit by using an available photodiode model in PC-based simulation program with integrated circuit emphasis to obtain a suitable output,the full chaotic circuit is verified with standard 0.6-μm complementary metal oxide semiconductor parameters.Chaotic dynamics are analyzed as a function of the light intensity under different control voltage levels.The time series,frequency spectra,transitions in state spaces,bifurcation diagrams and the largest Lyapunov exponent are improved.

Impact of Temperature Variation on Performance of Carbon Nanotube Field-Effect Transistor-Based on Chaotic Oscillator:A Quantum Simulation Study

We evaluate the impact of temperature on the output behavior of a carbon nanotube field effect transistor （CNFET） based chaotic generator. The sources cause the variations in both current-voltage characteristics of the CNFET device and an overall chaotic circuit is pointed out. To verify the effect of temperature variation on the output dynamics of the chaotic circuit, a simulation is performed by employing the CNFET compact model of Wong et al. in HSPICE with a temperature range from -100℃ to 100℃. The obtained results with time series, frequency spectra, and bifurcation diagram from the simulation demonstrate that temperature plays a significant role in the output dynamics of the CNFET-based chaotic circuit. Thus, temperature-related issues should be taken into account while designing a high-quality chaotic generator with high stability.

Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system

Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.

A new nonlinear oscillator with infinite number of coexisting hidden and self-excited attractors

In this paper,we introduce a new two-dimensional nonlinear oscillator with an infinite number of coexisting limit cycles.These limit cycles form a layer-by-layer structure which is very unusual.Forty percent of these limit cycles are self-excited attractors while sixty percent of them are hidden attractors.Changing this new system to its forced version,we introduce a new chaotic system with an infinite number of coexisting strange attractors.We implement this system through field programmable gate arrays.

Dynamical behaviors of a system with switches between the Rossler oscillator and Chua circuits

The behaviors of a system that alternates between the R¨ossler oscillator and Chua＇s circuit is investigated to explore the influence of the switches on the dynamical evolution.Switches related to the state variables are introduced,upon which a typical switching dynamical model is established.Bifurcation sets of the subsystems are derived via analysis of the related equilibrium points,which divide the parameters into several regions corresponding to different types of attractors.The dynamics behave typically in period orbits with the variation of the parameters.The focus/cycle periodic switching phenomenon is explored in detail to present the mechanism of the movement.The period-doubling bifurcation to chaos can be observed via the doubling increase of the turning points related to the switches.Furthermore,period-decreasing sequences have been obtained,which can be explained by the variation of the eigenvalues associated with the equilibrium points of the subsystems.

Dynamical Behaviors of a TiO_(2) Memristor Oscillator

We design a new chaotic oscillator based on the realistic model of the HP TiO_(2) memristor and Chua's circuit.Some basic dynamical behaviors of the oscillator,including equilibrium set,Lyapunov exponent spectrum and bifurcations with respect to various circuit parameters,are investigated theoretically and numerically.Chaotic attractors generated by the proposed oscillator are described with simulations and experiments,showing a good agreement.The main finding by analysis is that the proposed oscillator has no transient chaos and weak hyperchaos appears.Furthermore,its stability is insensitive to its initial values,thereby generating continuous and stable chaotic oscillation signals for chaos-based applications.

Research and Simulation on Weak Signal Detection Based on Duffing Oscillator and Damping Ratio Perturbation

The chaotic system is sensitive to the initial value, and this can be applied in the weak signal detection. There are periodic, critical and chaotic states in a chaotic system. When the system is in the critical state, a small perturbation of system,n parameter may lead to a qualitative change of the system＇s state. This paper introduces a new method to detect weak signals by the way of disturbing the damping ratio. The authors choose the duffing equation, using MATLAB to carry on the simulation, to study the changes of the system when the signal to be measured is added to the damping ratio. By means of observing the phase loots chart and time damin chart, the weak signal will be detected.

CHAOTIC OSCILLATION OF ANONLINEAR POWER SYSTEM

For a nonlinear power transmission system, the residue calculus method is introduced and applied to study its heteroclinic bifurcation. There a cone region and a strip region of parameters are obtained, in which the power transmission system displays chaotic oscillation. This gives a theoretic analysis and a computational method for the purpose to control the nonlinear system with deviation stably running.

Chaotic oscillations in a piecewise linear spring-mass system

Chaotic oscillations are useful in assessing the health of a structure. Hence, simple chaotic systems which can easily be realized mechanically or electro-mechanically are highly desired. We study a new pieeewise linear spring-tnass system. The chaotic behaviour in this system is characterized using bifurcation diagrams and the invariant parameters of the dynamics. We also show that there exists a stochastic analogue of this system, which mimics the dynamical features of its deterministic counterpart. This allows a greater flexibility in practical designs as the chaotic oscillations are obtained either deterministically or stochastically. Also, the oscillations are low dimensional, which reduces the computational resources needed for obtaining the invariant parameters of this system.

Temperature effects of GaAs/Al_(0.45)Ga_(0.55)As superlattices on chaotic oscillation

For widespectrum chaotic oscillation,superlattice cryptography is an autonomous controllable brand-new technology.Originating from sequential resonance tunneling of electrons,the chaotic oscillation is susceptible to temperature change,which determines the performance of superlattices.In this paper,the temperature effects of chaotic oscillations are investigated by analyzing the randomness of a sequence at different temperatures and explained with superlattice microstates.The results show that the bias voltage at different temperatures makes spontaneous chaotic oscillations vary.With the temperature of superlattices changing,the sequence dives in entropy value and randomness at specific bias.This work fills the gap in the study of temperature stability and promotes superlattice cryptography for practice.

Periodic and chaotic oscillations in mutual-coupled mid-infrared quantum cascade lasers

Dynamic states in mutual-coupled mid-infrared quantum cascade lasers(QCLs) were numerically investigated in the parameter space of injection strength and detuning frequency based on the Lang-Kobayashi equations model. Three types of period-one states were found, with different periods of injection time delay τ_(inj), 2τ_(inj), and reciprocal of the detuning frequency. Besides, square-wave, quasi-period, pulse-burst and chaotic oscillations were also observed. It is concluded that external-cavity periodic dynamics and optical modes beating are the mainly periodic dynamics. The interaction of the two periodic dynamics and the high-frequency dynamics stimulated by strong injection induces the dynamic states evolution.This work helps to understand the dynamic behaviors in QCLs and shows a new way to mid-infrared wide-band chaotic laser.

Current Oscillation and dc-Voltage-Controlled Chaotic Dynamics in Semiconductor Superlattices

We report a detailed theoretical study of current oscillation and de-voltage-controlled chaotic dynamics in doped GaAs/AlAs resonant tunneling superlattices under crossed electric and magnetic fields. When the superlattice is biased at the negative differential velocity region, current self-oscillation is observed with proper doping concentration. The current oscillation mode and oscillation frequency can be affected by the dc voltage bias, doping density, and magnetic field. When an ac electric field with fixed amplitude and frequency is also applied to the system, different nonlinear properties show up in the external circuit with the change of dc voltage bias. We carefully study these nonlinear properties with different chaos-detecting methods.

利用盲反卷积和混沌振子增强船舶辐射噪声解调线谱

针对经典解调方法中心频率、带宽选择困难和解调线谱受带外噪声干扰难以分辨等问题,提出采用盲反卷积和混沌振子方法抑制带外噪声,增强船舶噪声解调线谱。该方法通过Duffing振子预检宽带船舶噪声低频弱周期信号,随后将相应频率作为最小噪声幅值比反卷积(MNAD)方法的先验参数,利用MNAD方法自适应搜索解调频带得到可清晰分辨的高信噪比解调线谱。仿真和实测数据分析表明,该方法较经典解调方法和其他盲反卷积方法,可获取更佳的中心频率和滤波带宽,所得解调线谱的窄带信噪比DF值最高。

PMSM混沌系统无初始状态约束的固定时间有界控制

永磁同步电机(PMSM)是一种多变量、耦合性强的非线性系统,在实际运行过程中会出现混沌振荡。为了抑制PMSM系统的混沌,本文设计一种无初始状态约束的固定时间有界控制器。首先根据PMSM系统各个子系统的虚拟误差设计虚拟控制器,通过反步法推导得出控制器具有较高的抗干扰性能和鲁棒性,并证明时变反馈参数能够保证系统在到达有限时间收敛的同时达到渐近稳定,且稳定时间只与规定的边界有关。最后数值仿真通过调整控制系数k使系统能够在不同的初始状态下快速达到稳定,验证了所设计的控制器无论系统的初始状态如何,都能够使系统在2.8 s内达到稳定状态且输出收敛于给定的边界。

基于改进自适应协同控制方法的电力系统混沌控制

针对4阶混沌电力系统,该文提出一种具有快速收敛特性的自适应协同控制方案。首先基于Lyapunov稳定性定理和全局快速收敛理论,设计了一种具有快速收敛特性的协同控制器,该控制器可使宏变量快速到达不变流形并可以得到平滑无抖振的控制输入,实现宏变量的精确收敛。然后将所设计的控制器应用于4阶电力系统的混沌控制中。由于电力系统中的能量过剩会引起混沌振荡,在控制回路中引入储能装置,通过控制储能装置吸收电力系统中多余的有功功率来抑制其混沌振荡。在此基础上通过设计自适应律,消除了控制器设计过程中出现的复杂项,增加了控制器的实用性。最后通过数值仿真,验证了该控制方案的有效性与优越性。