Amplitude death in nonlinear oscillators with indirect coupling

We investigate the effect of frequency mismatch in two indirectly coupled Rössler oscillators and Hindmarsh–Rose neuron model systems. While identical systems show in-phase or out-of-phase synchronization states when coupled through a dynamic environment, mismatch in the internal frequencies of the systems drives them to a fixed point state, i.e., amplitude death. There is a region in the parameter space of the frequency mismatch and coupling strength where system shows amplitude death. The numerical results of Rössler system are also experimentally verified using piece-wise Rössler circuits.     

Time delay induced partial death patterns with conjugate coupling in relay oscillators

We investigate the dynamics of delay-coupled relay oscillators with conjugate (or dissimilar) coupling and find the partial death with the phase-flip transition. This phenomenon is quite general and occurs for the limit cycle as well as chaotic relay oscillators. In the regime of partial death, parts of the system oscillate with large amplitude, while other element stays at rest. Using the Stuart-Landau and Rössler oscillators, we demonstrate that partial amplitude death is a robust dynamical state in coupled oscillators. We also studied the mismatch delay and find different types of dynamical pattern with partial death.     

耦合分数阶双稳态振子的同步、反同步与振幅死亡

研究了耦合分数阶振子的同步、反同步和振幅死亡等问题. 基于P-R振子在特定参数下的双稳态特性, 利用最大条件Lyapunov指数、最大Lyapunov指数和分岔图等数值方法分析发现, 通过选取初始条件和耦合强度, 可以控制耦合振子呈现混沌同步、混沌反同步、全部振幅死亡同步、全部振幅死亡反同步和部 分振幅死亡等丰富的动力学现象. 基于蒙特卡罗方法的原理, 在初始条件相空间中随机选取耦合振子的初始位置, 计算不同耦合强度下耦合振子的全部振幅死亡态、部分振幅死亡态和非振幅死亡态的比例, 从统计学角度表征了耦合分数阶双稳态振子的动力学特征. 几种有代表性的双稳态振子的吸引域进一步证明了统计方法的计算结果. 关键词： 振幅死亡 吸引域 双稳态     

Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators

Experimental observations of time-delay-induced amplitude death in two coupled nonlinear electronic circuits that are individually capable of exhibiting limit-cycle oscillations are described. The existence of multiply connected death islands in the parameter space of coupling strength and time delay for coupled identical oscillators is established. The existence of such regions was predicted earlier on theoretical grounds [Phys. Rev. Lett. 80, 5109 (1998); Physica (Amsterdam) 129D, 15 (1999)]. The experiments also reveal the occurrence of multiple frequency states, frequency suppression of oscillations with increased time delay, and the onset of both in-phase and antiphase collective oscillations.     

Experimental evidence for amplitude death induced by a time-varying interaction

In this paper, we study the time-varying interaction in coupled oscillatory systems. For this purpose, we have designed a novel time-varying resistive network using an analog switch and inverter circuits. We have applied this time-varying resistive network to mutually coupled identical Chua's oscillators. When the resistances are varied in time, we find that amplitude death arises in coupled identical oscillators. This has been observed numerically as well as verified through hardware experiments.     

Understanding Partial P T $\mathcal {P}\mathcal {T}$ Symmetry as Weighted Composition Conjugation in Reproducing Kernel Hilbert Space: An application to Non-hermitian Bose-Hubbard Type Hamiltonian in Fock space

International Journal of Theoretical Physics - A new kind of symmetry behaviour introduced as partial $\mathcal {P}\mathcal {T}$ -symmetry(henceforth $\partial _{\mathcal {P}\mathcal {T}}$ ) is...     

Resurgence of oscillation in coupled oscillators under delayed cyclic interaction

This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from amplitude death state, we introduce asymmetry and feedback parameter in the cyclic coupling forms as a result of which the death region shrinks due to higher asymmetry and lower feedback parameter values for coupled oscillatory systems. Some analytical conditions are derived for amplitude death and revival of oscillations in two coupled limit cycle oscillators and corresponding numerical simulations confirm the obtained theoretical results. We also report that the death state and revival of oscillations from quenched state are possible in the network of identical coupled oscillators. The proposed mechanism has also been examined using chaotic Lorenz oscillator.     

Stability analysis and design of amplitude death induced by a time-varying delay connection

The present Letter considers amplitude death in a pair of oscillators coupled by a time-varying delay connection. A linear stability analysis is used to derive the boundary curves for amplitude death in a connection parameters space. The delay time can be arbitrarily long for certain amplitude of delay variation and coupling strength. A simple systematic procedure for designing such variation and strength is provided. The theoretical results are verified by a numerical simulation.     

Partial Wave Analysis of J/ψ Decays into ρρπ

The possible place to search for exotic states in J/ψ hadronic decays is in J/ψ →ρρπ. Because of the symmetry of identical particle and the symmetry of isospin, the physical analysis on this channel is quite complicated. In this paper, the method to use the partial wave analysis based on covariant helicity amplitude analysis to study the invariant mass spectrum of ρρπ and to find the evidence of exotic states in ρρπ spectrum is discussed. The decay amplitude for the decay sequence J/ψ→ρX, X →ρπ is given first. Then we discuss how to realize the identical particle symmetry and the isospin symmetry in the decay amplitude, which is the key point in the analysis of this channel. Then the total decay amplitude of this channel including all decay components is given. After that, how to identify the exotic states in the ρρπ spectrum is discussed. What is discussed in this paper is the theoretical basis on experimentally searching for exotic states at BEPC/BES.     

A novel mixed-synchronization phenomenon in coupled Chua’s circuits via non-fragile linear control

Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme.In this paper,a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua’s circuits connected in a drive-response configuration.In particular,in the mixed-synchronization regime,different state variables of the response system can evolve into complete synchronization,anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix.Using Lyapunov stability theory,we derive some sufficient criteria for achieving global mixed-synchronization.It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities (LMIs).Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.     

Entanglement-Assisted Classical Capacity of a Generalized Amplitude Damping Channel

The entanglement-assisted capacity of a generalized amplitude damping channel is investigated by using the properties of partial symmetry and concavity of mutual information. The numerical and analytical results of the entanglement-assisted capacity are obtained under certain conditions. It is shown that the entanglement-assisted capacity depends on the channel parameters representing the ambient temperature and dissipation, and the prior entanglement between sender and receiver can approximately double the classical capacity of the generalized amplitude damping channel.     

A conditional symmetric memristive system with amplitude and frequency control

By introducing a memristor into a chaotic system with a single non-quadratic term and substituting an absolute value function for conditional symmetry, a unique chaotic system is constructed. Firstly, the system shares a special structure of symmetry and conditional symmetry. Secondly, the amplitude and frequency of the system variables can be rescaled by the applied memristor. Interestingly it gives a new case of attractor control namely partial amplitude control and global frequency control. At last, as a new regime of extreme multistability, the memristive system shows relatively simple bifurcation according to the initial condition. This new class of chaotic system has never been reported to the best of our knowledge.

     

Effect of common noise on phase synchronization in coupled chaotic oscillators

We report a general phenomenon concerning the effect of noise on phase synchronization in coupled chaotic oscillators: the average phase-synchronization time exhibits a nonmonotonic behavior with the noise amplitude. In particular, we find that the time exhibits a local minimum for relatively small noise amplitude but a local maximum for stronger noise. We provide numerical results, experimental evidence from coupled chaotic circuits, and a heuristic argument to establish the generality of this phenomenon.     

Spherically Symmetric Solutions of Light Galileon

We have been studied the model of light Galileon with translational shift symmetry ? → ? + c. The matter Lagrangian is presented in the form \(\mathcal {L}_{\phi }= -\eta (\partial \phi )^{2}+\beta G^{\mu \nu }\partial _{\mu }\phi \partial _{\nu }\phi \). We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of \(f(R,R^{\mu \nu }T_{\mu \nu }^{m})\). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon’s field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ? = t, which it is remembered by us dilaton field.     

Forced(2+1)-dimensional discrete three-wave equation

We generalize the ■-dressing method to investigate a(2+1)-dimensional lattice,which can be regarded as a forced(2+1)-dimensional discrete three-wave equation.The soliton solutions to the(2+1)-dimensional lattice are given through constructing different symmetry conditions.The asymptotic analysis of one-soliton solution is discussed.For the soliton solution,the forces are zero.     

Complicated basins and the phenomenon of amplitude death in coupled hidden attractors

Understanding hidden attractors, whose basins of attraction do not contain the neighborhood of equilibrium of the system, are important in many physical applications. We observe riddled-like complicated basins of coexisting hidden attractors both in coupled and uncoupled systems. Amplitude death is observed in coupled hidden attractors with no fixed point using nonlinear interaction. A new route to amplitude death is observed in time-delay coupled hidden attractors. Numerical results are presented for systems with no or one stable fixed point. The applications are highlighted.     

Amplitude death in systems of coupled oscillators with distributed-delay coupling

This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributions. Analytical results are confirmed by numerical computation of the eigenvalues of the corresponding characteristic equations. These results indicate that larger widths of delay distribution increase the regions of amplitude death in the parameter space. In the case of a uniformly distributed delay kernel, for sufficiently large width of the delay distribution it is possible to achieve amplitude death for an arbitrary value of the average time delay, provided that the coupling strength has a value in the appropriate range. For a gamma distribution of delay, amplitude death is also possible for an arbitrary value of the average time delay, provided that it exceeds a certain value as determined by the coupling phase and the power law of the distribution. The coupling phase has a destabilizing effect and reduces the regions of amplitude death.     

From low-dimensional synchronous chaos to high-dimensional desynchronous spatiotemporal chaos in coupled systems

The dynamic behavior of coupled chaotic oscillators is investigated. For small coupling, chaotic state undergoes a transition from a spatially disordered phase to an ordered phase with an orientation symmetry breaking. For large coupling, a transition from full synchronization to partial synchronization with translation symmetry breaking is observed. Two bifurcation branches, one in-phase branch starting from synchronous chaos and the other antiphase branch bifurcated from spatially random chaos, are identified by varying coupling strength epsilon. Hysteresis, bistability, and first-order transitions between these two branches are observed.     

Soliton coupling in birefringent optical fiber with third-order dispersion

Nonlinear coupling of polarized solitons in birefringent optical fiber in the presence of third-order dispersion is considered in the framework of the coupled nonlinear Schrödinger equations. The influence of third-order dispersion on the interaction between solitons is investigated. For sufficiently strong third-order dispersion the interaction may even become repulsive. The stable conditions for solitons of partial pulses are analyzed and amplitude threshold, which decreases with third-order dispersion coefficient decreasing, for the capture of solitons of partial pulses into a coupled two-component pulse is obtained.     

New exact solutions of Einstein—Maxwell equations for magnetostatic fields

The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields, which is a coupled system of nonlinear partial differential equations of the second order. The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations. Some of the reduced systems are further studied to obtain the exact solutions.