Inverse Synchronization Research Articles

Generalized time-delay reverse synchronization with error feedback coefficients

To enhance the application of discrete chaotic systems in secure communication, we introduce a novel generalized time-delay inverse synchronization method with error feedback coefficient. This paper outlines the derivation of an inverse master-slave time-delay generalized synchronization system using the Lyapunov theory with error feedback coefficient design, which is proposed for the first time. To verify the efficacy of the synchronization method, we constructed a new 4D discrete hyperchaotic system. The dynamic properties of the novel system, such as the phase diagram and Lyapunov exponents, are investigated. Empirical outcomes reveal that generalized discrete time-delay synchronization can be accomplished under certain conditions for the error feedback coefficient. The study utilizes the chaotic masking technique to encrypt and decrypt messages in the secure communication system. The experimental findings reveal that by integrating the synchronization approach with the time-delay context of secure communication, the applicable design of the synchronization procedure is adaptable and trustworthy, catering to the pertinent requirements of engineering, and has the capacity to attain instantaneous chaotic synchronization requisites.

Research on the Synchronization Problem in the Combustion of Candles

In 2020, IYPT question 5 “synchronized candles” describes an interesting common phenomenon in life. The so-called synchronous candle refers to the flame that can be observed to oscillate when several adjacent candles are burning. Two such oscillations can be coupled with each other, leading to in-phase or reverse phase. In this paper, the control variable method is used to study the reason of the oscillation of a single oscillator and the phenomenon of inphase or anti phase oscillation of candles with different separation distance. It is found that the phenomenon of the oscillation coupling of regular candles is related to the distance between candles. Considering that the gas diffusion coefficient of the air is too low and the isotherm of the candle is relatively stable, the most likely cause of synchronization or inverse synchronization is thermal radiation. Finally, FDS software is used to simulate the combustion of the flame, and the results of in-phase and inverse vibration are also obtained.

The Implementation and Evaluation of Individual Preference in Robot Facial Expression Based on Emotion Estimation Using Biological Signals.

Recently, robot services have been widely applied in many fields. To provide optimum service, it is essential to maintain good acceptance of the robot for more effective interaction with users. Previously, we attempted to implement facial expressions by synchronizing an estimated human emotion on the face of a robot. The results revealed that the robot could present different perceptions according to individual preferences. In this study, we considered individual differences to improve the acceptance of the robot by changing the robot’s expression according to the emotion of its interacting partner. The emotion was estimated using biological signals, and the robot changed its expression according to three conditions: synchronized with the estimated emotion, inversely synchronized, and a funny expression. During the experiment, the participants provided feedback regarding the robot’s expression by choosing whether they “like” or “dislike” the expression. We investigated individual differences in the acceptance of the robot expression using the Semantic Differential scale method. In addition, logistic regression was used to create a classification model by considering individual differences based on the biological data and feedback from each participant. We found that the robot expression based on inverse synchronization when the participants felt a negative emotion could result in impression differences among individuals. Then, the robot’s expression was determined based on the classification model, and the Semantic Differential scale on the impression of the robot was compared with the three conditions. Overall, we found that the participants were most accepting when the robot expression was calculated using the proposed personalized method.

Function-based hybrid synchronization types and their coexistence in non-identical fractional-order chaotic systems

This paper presents new results related to the coexistence of function-based hybrid synchronization types between non-identical incommensurate fractional-order systems characterized by different dimensions and orders. Specifically, a new theorem is illustrated, which ensures the coexistence of the full-state hybrid function projective synchronization (FSHFPS) and the inverse full-state hybrid function projective synchronization (IFSHFPS) between wide classes of three-dimensional master systems and four-dimensional slave systems. In order to show the capability of the approach, a numerical example is reported, which illustrates the coexistence of FSHFPS and IFSHFPS between the incommensurate chaotic fractional-order unified system and the incommensurate hyperchaotic fractional-order Lorenz system.

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional-order chaotic systems

The topic related to the coexistence of different synchronization types between fractional-order chaotic systems is almost unexplored in the literature. Referring to commensurate and incommensurate fractional systems, this paper presents a new approach to rigorously study the coexistence of some synchronization types between nonidentical systems characterized by different dimensions and different orders. In particular, the paper shows that identical synchronization (IS), antiphase synchronization (AS), and inverse full state hybrid projective synchronization (IFSHPS) coexist when synchronizing a three-dimensional master system with a fourth-dimensional slave system. The approach, which can be applied to a wide class of chaotic/hyperchaotic fractional-order systems in the master-slave configuration, is based on two new theorems involving the fractional Lyapunov method and stability theory of linear fractional systems. Two examples are provided to highlight the capability of the conceived method. In particular, referring to commensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Rössler system of order 2.7 and the hyperchaotic four-dimensional Chen system of order 3.84. Finally, referring to incommensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Lü system of order 2.955 and the hyperchaotic four-dimensional Lorenz system of order 3.86.

Is it right to estimate inter-modular connectivity from local field potentials?

Human brains with hundreds of billions of neurons are organized in a hierarchical modular network. There have been many attempts to estimate inter-modular connectivity utilizing coherent neuronal activities of a huge number of neurons, such as the electro-encephalogram, the magneto-encephalogram, and the functional magnetic resonance imaging. Here we ask a question: Is the inter-modular connectivity estimated from the modular activities consistent with the inter-modular connectivity that could be extracted from the network connectivity of individual nodes? To answer this question, we introduce a method of estimating the inter-modular connectivity based on the analysis of inverse phase synchronization [1,2]. For coupled phase oscillators on a hierarchical modular network shown in the Figure 1(A), the local field potential corresponding to a module is defined as the mean phase of oscillators belonging to a subset of the module. Figure 1 (A) A hierarchical modular network model 256-p-q-r, where p denotes the number of links of one node with nodes of its lower-level module, q links with nodes of the rest modules in its upper-level module, and r links with nodes of any modules from the ... For strong coupling strength, it is shown in Figure 1(B) that the inverse phase synchronization index grows linearly with the number of links connecting two modules. This result enables us to estimate the inter-modular connectivity in various complex systems from the inverse phase synchronization index of the mesoscopic modular activities.

A general control method for inverse hybrid function projective synchronization of a class of chaotic systems

A general control method for inverse hybrid function projective synchronization of a class of chaotic systems

Synchronization and Inverse Synchronization of Some Different Dimensional Discrete-time Chaotic Dynamical Systems via Scaling Matrices

In this paper, new types of synchronization and inverse synchro-nization are proposed for some dierent dimensional chaotic dynamical systems in discrete-time using scaling matrices. Based on Lyapunov stability theory and nonlinear controllers, new synchronization results are derived. Numerical simulations are used to verify the eectiveness of the proposed schemes.

AN UNIVERSAL PHENOMENON IN MUTUALLY COUPLED CHUA'S CIRCUIT FAMILY

This paper presents the universality of the coexistence of complete synchronization with the recently new proposed inverse π-lag synchronization, in the case of mutually coupled systems of Chua's circuit family. The phenomenon of multistability and the nature of this circuit family systems are the key-points which lead to the explanation of this coexistence. For the need of this work, the most representative circuit of this circuits' family, the Chua oscillator, is used. Simulation results confirm this universality in the class of Chua's circuit family.

Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order

This paper mainly investigates a novel inverse projective synchronization between two different fractional‐order hyperchaotic systems, that is, the fractional‐order hyperchaotic Lorenz system and the fractional‐order hyperchaotic Chen system. By using the stability theory of fractional‐order differential equations and Lyapunov equations for fractional‐order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional‐order hyperchaotic Lorenz system and fractional‐order hyperchaotic Chen system are also successfully achieved, respectively. Finally, simulations are presented to demonstrate the validity and feasibility of the proposed method.

ANTI-PHASE AND INVERSE π-LAG SYNCHRONIZATION IN COUPLED DUFFING-TYPE CIRCUITS

The dynamic behavior of bidirectionally coupled Duffing-type circuits is numerically and experimentally investigated. Two related phenomena are explored such as anti-phase synchronization and inverse π-lag synchronization. Anti-phase synchronization is observed for the first time in coupled Duffing-type systems, while the inverse π-lag synchronization phenomenon in mutually coupled identical oscillators is a new type of synchronization. Inverse π-lag synchronization can be characterized by the vanishing of the sum of two relevant periodic signals. The first one is the signal of the first circuit x1and the second is the signal of the second circuit x2with a time lag τmin. This time lag is equal to T/2, where T is the period of x1and x2. The measurements and numerical computations suggest that these two synchronization phenomena are correlated with the symmetry under the transformation, x → -x, y → -y and t → t + T/2, which the Duffing equation exhibits.

Inverse synchronization of coupled fractional-order systems through open-plus-closed-loop control

In this paper, the inverse synchronization problem of fractional-order dynamical systems is investigated. A general explicit coupling via an open-plus-closed-loop control for inverse synchronization of two arbitrary unidirectionally or bidirectionally coupled fractional-order systems is proposed. The inverse synchronization is proved analytically based on the stability theorem of the fractional differential equations. A key feature of this proposed scheme is that it can be applied not only to nonchaotic but also to chaotic fractional-order systems whenever they exhibit regular or irregular oscillations. Feasibility of the proposed inverse synchronization scheme is illustrated through numerical simulations.

Synchronization and anti-synchronization of chaos in an extended Bonhöffer–van der Pol oscillator using active control

In this paper, we investigate the complete synchronization and anti-synchronization (AS) of double-scroll chaotic attractor exhibited by an extended Bonhöffer–van der Pol (BVP) oscillator, using active control technique. In both synchronization schemes, the oscillators show good transient performance; while the AS state is further shown to correspond with complete inverse synchronization. Numerical simulations are also presented to verify the theoretical results.

Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields

Identity synchronization is observed experimentally and numerically in the chaotic dynamics of a system of two unidirectionally coupled semiconductor lasers. The transmitter and receiver lasers are subjected to polarization-rotated optical feedback and injection, respectively. Numerical and analytical results show that identity synchronization requires parameter matching through a relationship between the injection and feedback strengths, and linewidth enhancement factors of the lasers. Inverse synchronization is also observed experimentally.

Complete inverse chaos synchronization, parameter mismatches and generalized synchronization in the multi-feedback Ikeda model

We investigate complete inverse synchronization between two uni-directionally coupled chaotic multi-feedback Ikeda systems and find its existence and stability conditions. We also study generalized synchronization between two uni-directionally coupled chaotic non-identical Ikeda models and obtain existence conditions for the generalized synchronization. Numerical simulations fully support the analytical findings. Generalization of the approach to the wider class of non-linear chaotic systems is also presented.

Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays

We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach.

Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers.

Synchronization of chaos is achieved experimentally in unidirectionally coupled external-cavity vertical-cavity surface-emitting semiconductor lasers operating in an open-loop regime. Synchronization is observed when the polarization of the transmitter is perpendicular to the polarization (x polarization) of the free-running receiver. The ratio of transmitter output to y-polarized receiver output power shows normal (positive-slope) synchronization. However, inverse (negative-slope) synchronization is found to arise between the transmitter output and the x-polarized receiver output power.

SC-CNNs for chaotic signal applications in secure communication systems.

In this paper a CNNs based circuit for the generation of hyperchaotic signals is proposed. The circuit has been developed for applications in secure communication systems. An Saito oscillator has been designed by using a suitable configuration of a four-cells State-Controlled CNNs. A cryptography system based on the Saito oscillator has been implemented by using inverse system synchronization. The proposed circuit implementation and experimental results are given.

Generalized synchronization of chaos in He-Ne lasers.

We experimentally demonstrate synchronization of chaos in one-way coupled He-Ne lasers with optical feedback. We observe different types of synchronization such as identical synchronization, inverse synchronization, and random amplification. These dynamics are maintained only for a short duration of several hundred milliseconds. We also observe generalized synchronization of chaos by using one master and two slave lasers. The generalized synchronization is achieved for a long duration of tens of seconds under injection locking. The generalized synchronization is always maintained while the injection locking is achieved.

Inverse synchronization of chaotic systems in an erbium-doped fibre dual-ring laser using the mutual coupling method

Inverse synchronization of chaos is a type of synchronization in which the dynamical variables of two chaotic systems are inversely equal. In this paper, we present a scheme for inverse synchronization of two chaotic systems in an erbium-doped fibre dual-ring laser using the mutual coupling method. For realistic values of the systems, we demonstrate two kinds of results, as follows. (1) Two independent identical chaotic systems can go into inversely synchronized chaotic oscillation for coupling greater than 0.03. (2) When some parameter of one system varies, the state of the coupled systems could go into some periodic states directly or by inverse bifurcation. Simultaneously, they will lose the synchronization as the parameter changes.