Adaptive Synchronization Approach Research Articles

Asymmetrical novel hyperchaotic system with two exponential functions and an application to image encryption

Abstract In this article, asymmetrical novel system with two exponential functions, which can show hyperchaotic behavior, has been proposed. Although new system possesses only one unstable equilibrium. The dynamical behaviors of such system are discovered by computing the Lyapunov exponents and bifurcation diagram. Furthermore, the synchronization of the proposed system are also presented by an adaptive synchronization approach of two identical hyperchaotic systems. An application to image encryption has been obtained.

The approximate lag and anticipating synchronization between two unidirectionally coupled Hindmarsh-Rose neurons with uncertain parameters

<p>This research presents an adaptive synchronization approach crafted to facilitate exact lag synchronization between a pair of unidirectionally linked Hindmarsh-Rose (HR) neurons, taking into account both explicit propagation delays and the existence of uncertain parameters. The precise condition for lag synchronization is deduced analytically, utilizing the Laplace transform and convolution theorem, alongside the iterative approach within the framework of Volterra integral equations theory. The established criterion guarantees robust stability irrespective of the propagation delay's magnitude, facilitating the realization of approximate lag and anticipating synchronization in a pair of HR neurons. The approximate synchronizations are realized in the absence of direct time-delay coupling, with the Taylor series expansion serving as an alternative to the precise time-delay component. Numerical simulations are executed to validate the effectiveness of the suggested approximate synchronization approach. The research demonstrates that employing the current state of an HR neuron, despite having uncertain parameters, enables the accurate prediction of future states and the reconstruction of past states. This study provides a novel perspective for comprehending neural processes and the advantageous attributes inherent in nonlinear and chaotic systems.</p>

An adaptive synchronization approach in a network composed of four neurons with energy diversity

An adaptive synchronization approach in a network composed of four neurons with energy diversity

Energy balance and synchronization via inductive-coupling in functional neural circuits

A reliable functional neural circuit can estimate the information encoding and signal exchange between neurons, and thus the recognition of electric activities in biological issues can be considered with problems on functional networks connected by neural circuits because more biophysical factors can be taken into account. Neurons communicate with each other via synaptic connections, besides the electric synapse connection via resistor coupling, inductor is effective to perform function as chemical synapses by activating similar inductive field coupling. In this paper, two kinds of neural circuits (light-sensitive and thermosensitive circuits) are connected by an induction coil, and external stimuli are applied to detect the adaptive synchronization approach when the coupling intensity is controlled by energy diversity between neurons. The two neurons hold different intrinsic energy values and then the synaptic connection is created for fast energy exchange along the coupling channel with increasing coupling intensity adaptively. When the energy of two neural circuits/neurons reaches perfect balance, the coupling intensity terminates its further increase and maintains a constant value. In case of phase synchronization/lock between neurons, desynchronization occurs accompanied by continuous energy pumping along the coupling channel without energy balance. Indeed, external energy injection can enhance the field coupling between neurons for decreasing the energy diversity. The involvement of memristive function as induction current for discerning electromagnetic induction in one neuron can increase the energy diversity between neurons, and then bursting synchronization can be suppressed. For the same and identical neural circuits, adaptive growth of synaptic connection can realize perfect energy balance and complete synchronization. For different neural circuits, synchronization is corrupted even the field coupling is further enhanced in the intensity. As a result changeable energy diversity is helpful to induce desynchronization and potential neural disorders and diseases can be blocked.

A New 4D Hyperchaotic System with Dynamics Analysis, Synchronization, and Application to Image Encryption

In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. Exhaustive dynamic analyses of the novel hyperchaotic model using several dynamical studies are described. The dynamics of the system considered are first investigated analytically and numerically to explore phenomena and the selection of hyperchaotic behavior utilized for designing image cryptosystem. Since the proposed hyperchaotic model has rich dynamics, it displays hidden attractors. It emerges from this dynamic the existence of a single unstable equilibrium point giving rise to self-excited attractors, hysteresis phenomenon, and hyperchaotic behavior strongly recommended for securing information by its character. Furthermore, the feasibility and synchronization of the proposed system are also presented by developing, respectively, Raspberry surveys and an adaptive synchronization approach of two identical hyperchaotic systems. By employing the hyperchaotic behavior of the 4D map, an image encryption scheme is proposed as well. It is one round of a pixel-based permutation and a bit-wise diffusion phase. The secret key of the 4D map is derived from the SHA-256 value of the input image. It acts as the signature of the input image. Hence, the secret key exhibits high sensitivity to single-bit alteration in the image, which makes the cryptosystem robust against chosen/known-plaintext attacks. Performance analyses prove that the proposed cryptosystem provides the best in terms of the performance/complexity trade-off, as compared to some recently published algorithms.

The adaptive synchronization of fractional-order chaotic system with fractional-order $$\varvec{1}<\varvec{q}<\varvec{2}$$ 1 < q < 2 via linear parameter update law

This paper presents an adaptive synchronization approach for fractional-order chaotic systems with fractional-order $$1<q<2$$ and unknown system parameters based on the Mittag–Leffler function and the generalized Gronwall inequality. A sufficient condition is obtained. The numerical simulations are given to verify the effectiveness of this synchronization scheme.

One adaptive synchronization approach for fractional-order chaotic system with fractional-order 1 < q < 2.

Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme.

Synchronization of delayed reaction–diffusion neural networks via an adaptive learning control approach

An adaptive learning control strategy is utilized to investigate the synchronization problem for delayed reaction–diffusion neural networks (RDNNs) with unknown time-varying coupling strengths. A novel adaptive synchronization approach is proposed, which is consisted of differential–difference type updating law and feedback control law. By constructing a Lyapunov–Krasovskii-like composite energy functional (CEF), based on the LaSalle invariant principle of functional differential equations, a sufficient condition for the adaptive synchronization of such a system is obtained. Finally, a numerical example is given to show the effectiveness of the proposed synchronization method.

Adaptive Hybrid Function Projective Synchronization of Chaotic Systems with Time‐Varying Parameters

The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time‐varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time‐varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage‐like adaptation law is also proposed to guarantee the ultimately uni‐formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme.

Synchronization of hyperchaotic Chen systems: a class of the adaptive control approach

The synchronization of hyperchaotic Chen systems is considered. An adaptive synchronization approach and a cascade adaptive synchronization approach are presented to synchronize a drive system and a response system. By utilizing an adaptive controller based on the dynamic compensation mechanism, exact knowledge of the systems is not necessarily required, and the synchronous speed is controllable by tuning the controller parameters. Sufficient conditions for the asymptotic stability of the two synchronization schemes are derived. Numerical simulation results demonstrate that the adaptive synchronization scheme with four control inputs and the cascade adaptive synchronization scheme with only one control signal are effective and feasible in chaos synchronization of hyperchaotic systems.

Dynamical parameter identification from a scalar time series

If a drive system with unknown parameters represents "reality" and the response system a "computational model," the unidirectional coupling can be used to change model parameters, as well as the model state, such that both systems synchronize with each other and model parameters coincide with their true values of "reality." Such a parameter identification method is called adaptive synchronization (also autosynchronization) method and is widely used in the literature. Because one usually cannot find proper parameter update rules by exploiting information obtained from only a scalar time series, parameter identification with adaptive synchronization from a scalar time series is not well understood and still remains challenging until now. In this paper we introduce a novel adaptive synchronization approach with an effective guidance parameter to update rule design. This method includes three steps: (i) finding some proper control signals such that the "computational model" synchronizes with the "real" system if no parameter mismatch exists (that is, both systems have identical parameters); (ii) designing parameter update rules in terms of a necessary condition for ensuring local synchronization; and (iii) determining the value for each parameter update rate for ensuring the local stability of autosynchronization manifold according to the conditional Lyapunov exponents method. The reliability of the suggested technique is illustrated with the Lorenz system and a unified chaotic model.

Robust adaptive global synchronization of complex dynamical networks by adjusting time-varying coupling strength

A new robust adaptive synchronization approach for the global synchronization of complex dynamical networks is proposed. Both the characteristics of the uncoupled nodes of the network and the coupling matrix are unknown, but only a time-varying coupling strength is used in this paper. Based on the LaSalle–Yoshizawa theorem and by introducing an update law, a sufficient condition of the global synchronization is obtained. The update law is only dependent on the states of the complex dynamical network, which do not need any other information such as the characteristic of the uncoupled nodes of the network and the second largest eigenvalue of the coupling matrix. Compared with the existing results, our synchronization strategy is still useful when the existing synchronization methods become invalid. Moreover, it is very convenient to use. An example of the complex network is finally used to verify the proposed theoretical result.

Fuzzy model-based adaptive synchronization of time-delayed chaotic systems

In this paper, fuzzy model-based synchronization of a class of first order chaotic systems described by delayed-differential equations is addressed. To design the fuzzy controller, the chaotic system is modeled by Takagi–Sugeno fuzzy system considering the properties of the nonlinear part of the system. Assuming that the parameters of the chaotic system are unknown, an adaptive law is derived to estimate these unknown parameters, and the stability of error dynamics is guaranteed by Lyapunov theory. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.

Adaptive Synchronization of Uncertain Chaotic Systems Based on T–S Fuzzy Model

This paper presents an adaptive approach for synchronization of Takagi-Sugeno (T-S) fuzzy chaotic systems. T-S fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive system. Since the output of the drive system is only available for synchronization, the response system is designed based on fuzzy adaptive observer for uncertain parameters and parameter mismatch cases. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov stability theory and derive stability conditions by solving linear matrix inequalities (LMIs) problem. The adaptive law is derived to estimate the uncertain parameters or parameter mismatch. Numerical examples are given to demonstrate the validity of the proposed fuzzy adaptive synchronization approach.

T-S 퍼지 모델을 이용한 불확실한 카오스 시스템의 적응동기화

본 논문은 퍼지 모델을 이용한 불확실한 카오스 시스템의 적응 동기화 기법을 제안한다. 카오스 동기화 시스템은 마스터 시스템과 슬레이브 시스템으로 구성되며 각각의 시스템은 Takagi-Sugeno (T-S) 퍼지 모델을 통해 표현된다. 마스터 시스템은 파라미터가 미리 알려지지 않은 불확실한 모델로 가정되므로 불확실한 파라미터를 추정하기 위해 적응 기법을 적용하여 슬레이브 시스템을 설계한다. 동기화 오차 시스템을 안정화하고 불확실한 파라미터를 추정하는 적응 규칙을 이용한 제어기를 설계하며 Lyapunov 이론을 통해 안정도를 해석한다. 제안된 퍼지 적응 동기화 기법의 효과를 확인하기 위해서 Duffing 시스템과 Lorenz 시스템에 대해 모의 실험을 수행한다. This paper presents a fuzzy model-based adaptive approach for synchronization of chaotic systems which consist of the drive and response systems. Takagi-Sugeno (T-S) fuzzy model is employed to represent the chaotic drive and response systems. Since the parameters of the drive system are assumed unknown, we design the response system that estimates the parameters of the drive system by adaptive strategy. The adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. In addition, the controller in the response system contains two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples, including Doffing oscillator and Lorenz attractor, are given to demonstrate the validity of the proposed adaptive synchronization approach.

Fuzzy adaptive synchronization of uncertain chaotic systems

This Letter presents an adaptive approach for synchronization of Takagi–Sugeno (T–S) fuzzy chaotic systems. Since the parameters of chaotic system are assumed unknown, the adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. The control law to be designed consists of two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.

Adaptive synchronization of T–S fuzzy chaotic systems with unknown parameters

Abstract This paper presents a fuzzy model-based adaptive approach for synchronization of chaotic systems which consist of the drive and response systems. Takagi–Sugeno (T–S) fuzzy model is employed to represent the chaotic drive and response systems. Since the parameters of the drive system are assumed unknown, we design the response system that estimates the parameters of the drive system by adaptive strategy. The adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. In addition, the controller in the response system contains two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples, including Duffing oscillator and Lorenz attractor, are given to demonstrate the validity of the proposed adaptive synchronization approach.