A concept of coupled chaotic synchronous observers for nonlinear and adaptive observers-based chaos synchronization

Siddique, Muhammad; Rehan, Muhammad

doi:10.1007/s11071-016-2643-2

Cited by 24 publications

(10 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The FHN neuron model (for biophysical details, see [55]) has been extensively used to investigate many complex dynamical behaviors occurring in neuroscience [56][57][58][59][60]. For our investigation of SISR, we consider the following version of the FHN neuron model written on the slow timescale τ as…”

Section: Model Equationmentioning

confidence: 99%

Coherent neural oscillations induced by weak synaptic noise

Yamakou

Jost

2018

Nonlinear Dyn

View full text Add to dashboard Cite

We analyze the effect of synaptic noise on the dynamics of the FitzHugh-Nagumo (FHN) neuron model. In our deterministic parameter regime, a limit cycle solution cannot emerge through a singular Hopf bifurcation, but such a limit cycle can nevertheless arise as a stochastic effect, as a consequence of weak synaptic noise in a regime of strong timescale separation (ε → 0) between the slow and fast variables of the model. We investigate the mechanism behind this phenomenon, known as self-induced stochastic resonance (SISR) (Muratov et al. in Physica D 210:227-240, 2005), by using multiple-time perturbation techniques and by analyzing the escape mechanism of the random trajectories from the stable manifolds of the model equation. Even though SISR occurs only in the limit as the singular parameter ε → 0, decreasing ε does not increase the coherence of the oscillations in the FHN model, but rather increases the interval of the noise amplitude σ for which coherence occurs. This is in contrast to the dynamical system studied in Mura- 2005). Moreover, the phenomenon is robust under parameter tuning. Numerical simulations exhibit the results predicted by the theoretical analysis. In fact, our analysis together with that in Yamakou and Jost (Weak noise-induced transitions with inhibition and modulation of neural oscillations, 2017) reveals that the FHN model can support different stochastic resonance phenomena. While it had been known (Pikovsky and Kurths in Phys Rev Lett 78:775-778, 1997) that coherence resonance can occur when the slow variable is subjected to noise, we show that, when noise is added to the fast variable, two other types, inverse stochastic resonance and SISR, may emerge in the same weak noise limit and that the transition between these phenomena can be induced by varying a simple parameter.

show abstract

Section: Model Equationmentioning

confidence: 99%

Coherent neural oscillations induced by weak synaptic noise

Yamakou

Jost

2018

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…Siddique et al used a chaotic master–slave system with unknown parameters, bounded delay rates, finite time-delay, and perturbations to investigate the synchronization phenomenon by developing local adaptive and robust adaptive control methodologies 62 . Siddique and Rehan proposed observer-based control strategies to realize synchronization in drive and response chaotic systems 63 . Jia et al proposed a time-delayed coupled FHN system and studied its stability and Hopf bifurcation 58 .…”

Section: Introductionmentioning

confidence: 99%

Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control

Ibrahim

Kamran

Mannan

et al. 2021

Sci Rep

View full text Add to dashboard Cite

Synchronization plays a significant role in information transfer and decision-making by neurons and brain neural networks. The development of control strategies for synchronizing a network of chaotic neurons with time delays, different direction-dependent coupling (unidirectional and bidirectional), and noise, particularly under external disturbances, is an essential and very challenging task. Researchers have extensively studied the synchronization mechanism of two coupled time-delayed neurons with bidirectional coupling and without incorporating the effect of noise, but not for time-delayed neural networks. To overcome these limitations, this study investigates the synchronization problem in a network of coupled FitzHugh–Nagumo (FHN) neurons by incorporating time delays, different direction-dependent coupling (unidirectional and bidirectional), noise, and ionic and external disturbances in the mathematical models. More specifically, this study investigates the synchronization of time-delayed unidirectional and bidirectional ring-structured FHN neuronal systems with and without external noise. Different gap junctions and delay parameters are used to incorporate time-delay dynamics in both neuronal networks. We also investigate the influence of the time delays between connected neurons on synchronization conditions. Further, to ensure the synchronization of the time-delayed FHN neuronal networks, different adaptive control laws are proposed for both unidirectional and bidirectional neuronal networks. In addition, necessary and sufficient conditions to achieve synchronization are provided by employing the Lyapunov stability theory. The results of numerical simulations conducted for different-sized multiple networks of time-delayed FHN neurons verify the effectiveness of the proposed adaptive control schemes.

show abstract

“…Over the past decade, many scholars have studied the stability problem of nonlinear dynamical systems and obtained some extraordinary nice conclusions [1]- [20], and these research results have been fully reflected in the practical application [5]- [7]. Among these, the most representative is the good application of chaos in secure communication field, biology field, medicine field and etc [8]- [10].…”

Section: Introductionmentioning

confidence: 99%

“…It is mainly because as the special behavior of nonlinear dynamical systems, Chaotic time series have the characteristics of extreme sensitivity to the initial value, wide power spectrum and noise like characteristic, which makes the chaotic time series' characteristic have the feature of unpredictable and hidden. Now, synchronization and control of chaotic systems have become a hot topic, and then a variety of chaotic synchronization methods have been proposed, such as coupling synchronization method [1], variable structure synchronization method [2], adaptive synchronization method [3], linear and nonlinear feedback synchronization method [4]- [6], pulse synchronous method [7], [8], projective synchronization method [9], [10], fractional synchronization method [11] and the other methods [12]- [31]. Actually, most of the present methods which have been proposed focus on how to make the two chaotic systems asymptotically achieve synchronization, but the research on the optimization of chaotic synchronization rate is still relatively rare.…”

Section: Introductionmentioning

confidence: 99%

The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application

Li¹

2017

ACM

View full text Add to dashboard Cite

This paper studies the global exponential stability for a class of nonlinear dynamical systems. A new state feedback controller is designed, which can effectively stabilize this kind of nonlinear system to the equilibrium point at exponential rate. The feasibility of the method is proved theoretically, and an algorithm is systematically proposed to configure the related parameters of the controller. Then simulation results show the effectiveness of the proposed control method.

show abstract

A concept of coupled chaotic synchronous observers for nonlinear and adaptive observers-based chaos synchronization

Cited by 24 publications

References 36 publications

Coherent neural oscillations induced by weak synaptic noise

Coherent neural oscillations induced by weak synaptic noise

Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control

The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application

Contact Info

Product

Resources

About