Nonidentical Coupling Research Articles

Asymmetry in the Kuramoto model with nonidentical coupling.

Synchronization and desynchronization of coupled oscillators appear to be the key property of many physical systems. It is believed that to predict a synchronization (or desynchronization) event, the knowledge on the exact structure of the oscillatory network is required. However, natural sciences often deal with observations where the coupling coefficients are not available. In the present paper we suggest a way to characterize synchronization of two oscillators without the reconstruction of coupling. Our method is based on the Kuramoto chain with three oscillators with constant but nonidentical coupling. We characterize coupling in this chain by two parameters: the coupling strength s and disparity σ. We give an analytical expression of the boundary s_{max} of synchronization occurred when s>s_{max}. We propose asymmetry A of the generalized order parameter induced by the coupling disparity as a new characteristic of the synchronization between two oscillators. For the chain model with three oscillators we present the self-consistent inverse problem. We explore scaling properties of the asymmetry A constructed for the inverse problem. We demonstrate that the asymmetry A in the chain model is maximal when the coupling strength in the model reaches the boundary of synchronization s_{max}. We suggest that the asymmetry A may be derived from the phase difference of any two oscillators if one pretends that they are edges of an abstract chain with three oscillators. Performing such a derivation with the general three-oscillator Kuramoto model, we show that the crossover from the chain to general network of oscillators keeps the interrelation between the asymmetry A and synchronization. Finally, we apply the asymmetry A to describe synchronization of the solar magnetic field proxies and discuss its potential use for the forecast of solar cycle anomalies.

Synchronization analysis of linear time-varying matrix-weighted coupled systems and its applications

In this paper, we study the synchronization problem of continuous-time linear systems under time-varying matrix-weighted coupling. With the help of the notion of persistent excitation and an adapted stability result in adaptive control, we establish two sufficient exponential synchronization conditions using the connectivity of the persistent graph and the joint connectivity of the instantaneous time-varying graphs. The conditions recover those for the single-integrator consensus model with scalar-valued coupling. The results are further applied to solve the synchronization problem of continuous-time linear systems with time-varying and nonidentical coupling matrices, extending the existing conclusions in the literature. Finally, numerical examples are given to verify the derived results.

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

ABSTRACTThis paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.

Simultaneous All-Optical or and xor Logic Gates Based on the Bimodal Photonic Cavity Containing a Quantum Dot

We theoretically present a design for simultaneous all-optical or and xor logic gates based on single quantum dot (QD)-bimodal cavity system working in low-photon-number regime. The coupling between the QD and two degenerate cavity modes establishes new indirect excitation paths. Driven by single pulsed laser, both mode transmissions are observed. The delay between the peaks of the transmitted pulses is regarded as the extra transition interval (ETI) in the indirect path. When driven by two orthogonally polarized pulsed lasers with delay same as ETI, the coupling system suppresses the latter mode transmission due to the destructive interference effect. The or and xor logic gates based on presence of light are built and the function can be switched between two detectors by simply adjusting the driving pulse sequence. The results show that the proposed logic gates work well within a large range for coupling strength with comparable cavity decay rate. When taking two nonidealities (the detuning between two cavity modes and nonidentical coupling strengths) into consideration, the proposed system shows acceptable tolerances. Moreover, the robustness of the performance on parameters of the driving lasers, including pulse delay, width of pulse, absolute driving strength, and relative driving strength ratio, are demonstrated.

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor 𝜃 and relative coupling strength R=g 1/g 2 on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ a ),C(ρ f ),S(ρ a )) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate 𝜃 and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.

Interplay between interaction and nonidentical coupling for a Bose–Einstein Condensate in a triple-well potential

We investigate the effect of interaction and nonidentical coupling on the tunneling dynamics of a Bose–Einstein Condensate trapped in a triple-well potential. In certain parameter regions, we find a “two negatives make a positive” effect. While interaction or nonidentical coupling by itself can suppress the tunneling between the wells, both together enhance the tunneling. In addition, it is shown that under appropriate conditions, the mean-field dynamics displays beating phenomenon in the weak interaction regime. We present a physical explanation for such beating phenomenon. The effect of quantum fluctuation on the beating structure is also discussed numerically.

Inner and outer synchronization between two coupled networks with interactions

In this paper, we study two types of synchronization between two coupled networks with interactions, including inner synchronization inside each network and outer synchronization between two networks with the adaptive controllers. By Barbalat׳s lemma and linear matrix inequality (LMI), we obtain a sufficient condition for each network to be asymptotic stability in terms of LMI. When the inner synchronization happens inside each network, while outer synchronization does not appear, we design the adaptive controllers to realize the inner and outer synchronization simultaneously, and investigate the identical or nonidentical coupling and interactive matrices. We then obtain a theorem for the outer synchronization with the adaptive controllers. Finally we give some numerical examples to show the effectiveness of our obtained results. Our findings would provide insights into the dynamics of coupled networks with diverse connections.

Modulation of synchronization dynamics in a network of self-sustained systems

This paper addresses the combined modulatory effects of non-nearest neighbor oscillators and local injection on synchronized states dynamics with their corresponding stability boundaries in a network of self-sustained systems. The Whittaker method and Floquet theory are used to predict analytically the stability of these states for identical and non-identical coupling parameters. Charts revealing the modulation of synchronized states and their stability boundaries at the second order of interaction in the cases of identical and non-identical coupling parameters are constructed with and without an external signal locally injected in the network. Numerical simulations validate and complement the results of analytical surveys. The limits of the stability regions are numerically explored when a small amount of Gaussian white noise is also injected in the network.

Synchronization of Complex Dynamical Networks with Nonidentical Nodes and Derivative Coupling via Distributed Adaptive Control

Adaptive synchronization control is proposed for a new complex dynamical network model with nonidentical nodes and nonderivative and derivative couplings. The distributed adaptive learning laws of periodically time-varying and constant parameters and distributed adaptive control are designed. The new method which can obtain the synchronization error of closed-loop complex network system is asymptotic convergence in the sense of square error norm. What is more, the coupling matrix is not assumed to be symmetric or irreducible. Finally, a simulation example shows the feasibility and effectiveness of the approach.

Implementation of the Fredkin gate with a three-qubit mixed-spin Heisenberg model

We show that a local unitary (LU) equivalent Fredkin gate can be obtained from the free evolution of three mixed-spin qubits by virtue of numerical simulation with only one step. The spin-1 qubit acts as the control qubit, and two spin-1/2 qubits, which interact with the spin-1 qubit via the first neighbor spin interaction, respectively, play the role of target qubits. We also examine the imperfect Fredkin gate operation by considering the effects of nonidentical coupling constants, uniform and inhomogeneous magnetic fields.

Generation of an N-qubit phase gate via atom—cavity nonidentical coupling

A scheme for approximate generation of an N-qubit phase gate is proposed in cavity QED based on nonidentical coupling between the atoms and the cavity. The atoms interact with a highly detuned cavity-field mode, but quantum information does not transfer between the atoms and cavity field, and thus the cavity decay is negligible. The gate time does not rise with an increase in the number of qubits. With the choice of a smaller odd number l (related to atom–cavity coupling constants), the phase gate can be generated with a higher fidelity and a higher success probability in a shorter time (the gate time is much shorter than the atomic radiative lifetime and photon lifetime). When the number of qubits N exceeds certain small values, the fidelity and success probability rise slowly with an increase in the number of qubits N. When N → ∞, the fidelity and success probability infinitely approach 1, but never exceed 1.

Free-running period of neurons in the suprachiasmatic nucleus: Its dependence on the distribution of neuronal coupling strengths

The suprachiasmatic nucleus (SCN) pacemaker shows a free-running period ranging from 20 to 28 h for different species, which was usually explained from the angle of coupling strength. Based on the assumption of nonidentical coupling strengths in SCN, we find an alternative mechanism that the diversity of free-running period can be also caused by the distribution of coupling strengths. The free-running period is proportional to the average coupling strength and inverse proportional to the dispersion of couplings. Moreover, we present an analytic phase model to confirm our finding, which shows a solid foundation of our finding and opens a window to study the collective behaviors of SCN oscillators.

Transmission of information and synchronization in a pair of coupled chaotic circuits: An experimental overview

We propose a rationale for experimentally studying the intricate relationship between the rate of information transmission and synchronization level in active networks, applying theoretical results recently proposed. We consider two non-identical coupled Chua’s circuit with non-identical coupling strengths in order to illustrate the proceeding for experimental scenarios of very few data points coming from highly non-coherent coupled systems, such that phase synchronization can only be detected by methods that do not rely explicitely on the calculation of the phase. A relevant finding is to show that for the coupled Chua’s circuit, the larger the level of synchronization the larger the rate of information exchanged between both circuits. We further validate our findings with data from numerical simulations, and discuss an extension to arbitrarily large active networks.

Scheme for Implementing an N-Qubit Phase Gate via Selective Atom–Field Interaction with Cavity Quantum Electrodynamics

A scheme for implementing a two-qubit phase gate with atoms sent through a high-Q optical cavity is proposed by choosing nonidentical coupling constants between the atoms and cavity. The atomic spontaneous emission can be suppressed due to the large atom-field detuning. Moreover, the scheme can be generalized to implement an N-qubit phase gate and the gating time does not change with an increase of the number of qubits.

Efficient scheme for implementing anN-qubit Toffoli gate by a single resonant interaction with cavity quantum electrodynamics

A scheme for implementing a three-qubit Toffoli gate with atoms sent through a microwave cavity is proposed by choosing nonidentical coupling constants between the atoms and cavity. The scheme can be generalized to implement an $N$-qubit Toffoli gate and the gating time does not change with an increase of the number of qubits.

Invaded cluster algorithm for critical properties of periodic and aperiodic planar Ising models

We demonstrate that the invaded cluster algorithm, recently introduced by Machta et al, is a fast and reliable tool for determining the critical temperature and the magnetic critical exponent of periodic and aperiodic ferromagnetic Ising models in two dimensions. The algorithm is shown to reproduce the known values of the critical temperature on various periodic and quasiperiodic graphs with an accuracy of more than three significant digits. On two quasiperiodic graphs which were not investigated in this respect before, the twelvefold symmetric square-triangle tiling and the tenfold symmetric T\"ubingen triangle tiling, we determine the critical temperature. Furthermore, a generalization of the algorithm to non-identical coupling strengths is presented and applied to a class of Ising models on the Labyrinth tiling. For generic cases in which the heuristic Harris-Luck criterion predicts deviations from the Onsager universality class, we find a magnetic critical exponent different from the Onsager value. But also notable exceptions to the criterion are found which consist not only of the exactly solvable cases, in agreement with a recent exact result, but also of the self-dual ones and maybe more.

Extension of the theorem on the separation of a system of coupled differential equations

We develop the idea presented in a previous paper by including the case of non-identical coupling terms and show that, under some conditions, separation of the equations is also possible.