Interlayer antisynchronization in degree-biased duplex networks

With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most of these previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients can not destroy intralayer synchronization.Comment: 16 pages, 5 figures (Accepted for publication in the journal Physical Review E

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

This article presents an adaptive integral sliding mode control (SMC) design method for parameter identification and hybrid synchronization of chaotic systems connected in ring topology. To employ the adaptive integral sliding mode control, the error system is transformed into a special structure containing nominal part and some unknown terms. The unknown terms are computed adaptively. Then the error system is stabilized using integral sliding mode control. The controller of the error system is created that contains both the nominal control and the compensator control. The adapted laws and compensator controller are derived using Lyapunov stability theory. The effectiveness of the proposed technique is validated through numerical examples

Synchronization Phenomena in Coupled Birkhoff-Shaw Chaotic Systems Using Nonlinear Controllers

In this chapter, the well-known non-autonomous chaotic system, the Birkhoff-Shaw, which exhibits the structure of beaks and wings, typically observed in chaotic neuronal models, is used in a coupling scheme. The Birkhoff-Shaw system is a second-order non-autonomous dynamical system with rich dynamical behaviour, which has not been sufficiently studied. Furthermore, the master-slave (unidirectional) coupling scheme, which is used, is designed by using the nonlinear controllers to target synchronization states, such as complete synchronization and antisynchronization, with amplification or attenuation in chaotic oscillators. It is the first time that the specific method has been used in coupled non-autonomous chaotic systems. The stability of synchronization is ensured by using Lyapunov function stability theorem in the unidirectional mode of coupling. The simulation results from system’s numerical integration confirm the appearance of complete synchronization and antisynchronization phenomena depending on the signs of the parameters of the error functions. Electronic circuitry that models the coupling scheme is also reported to verify its feasibility

Generalized Synchronization of Different Chaotic Systems Based on Nonnegative Off-Diagonal Structure

The generalized synchronization problem is studied in this paper for different chaotic systems with the aid of the direct design method. Based on Lyapunov stability theory and matrix theory, some sufficient conditions guaranteeing the stability of a nonlinear system with nonnegative off-diagonal structure are obtained. Then the control scheme is designed from the stable system by the direct design method. Finally, two numerical simulations are provided to verify the effectiveness and feasibility of the proposed method

Probing the spectral density of a dissipative qubit via quantum synchronization

The interaction of a quantum system, which is not accessible by direct measurement, with an external probe can be exploited to infer specific features of the system itself. We introduce a probing scheme based on the emergence of spontaneous quantum synchronization between an out-of-equilibrium qubit, in contact with an external environment, and a probe qubit. Tuning the frequency of the probe leads to a transition between synchronization in phase and antiphase. The sharp transition between these two regimes is locally accessible by monitoring the probe dynamics alone and allows one to reconstruct the shape of the spectral density of the environment

Complex Projective Synchronization in Drive-Response Stochastic Complex Networks by Impulsive Pinning Control

The complex projective synchronization in drive-response stochastic coupled networks with complex-variable systems is considered. The impulsive pinning control scheme is adopted to achieve complex projective synchronization and several simple and practical sufficient conditions are obtained in a general drive-response network. In addition, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical simulations are provided to show the effectiveness and feasibility of the proposed methods