Synchronization, Multiresonance Phenomena, and Discrete Oscillation Periods in a Hopfield Neural Network with Two Time Delays

Rozier, Kelvin; Bondarenko, Vladimir E.

doi:10.1142/s0218127422500663

“…Networks are usually affected by stochastic factors, delays, nonlinear relative, such as stochastic time-delay nonlinear networks [20] and stochastic time-delay neural networks [21]. Similarly, multilayer Cohen Grossberg neural networks are also affected by random factors, nonlinear, and delays.…”

Section: Introductionmentioning

confidence: 99%

Stochastic fixed-time quantitative synchronization for multilayer derivative dynamic Cohen–Grossberg networks and secure communication

Tan

¹

,

Zhou

²

,

Lu

³

et al. 2023

Soft Comput

1

0

View full text Add to dashboard Cite

The implementation of fixed-time synchronization is a challenging problem for dynamic networks with derivative links. When there are derivative links in multilayer heterogeneous dynamic networks, it is difficult to obtain the fixedtime stable synchronization criteria via using the conventional Lyapunov function. So we choose a special Lyapunov function to solve the fixed-time stable synchronization criteria. In this paper, different from the comprehensive method used in lots of literature, to design and solve the fixed time controller, we use the analysis method to design a fixed time control strategy. When this strategy is used for the fixed-time synchronization of multilayer Heterogeneous networks with Cohen-Grossberg neural subnet, it will result in the designed controller does not contain differential terms, so as to reduce the difficulty in the design of fixed time controller. To be closer to reality, we consider multilayer neural networks with stochastic disturbances and nonlinear connections. When designing the controller, considering the actual communication constraints, we introduce quantization into the designed controller. Under the theoretical framework, we find that the upper limit for function of synchronization time is related to the quantization intensity, parameters of the designed Lyapunov function, parameters of the controller and a maximum eigenvalue related to the structure of multilayer Cohen-Grossberg neural networks. Finally, a simulation is supported to illustrate the effective of the derived theoretical framework.

show abstract

Role of asymmetry and external noise in the development and synchronization of oscillations in the analog Hopfield neural networks with time delay

Rozier,

Chechkin,

Bondarenko

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

0

View full text Add to dashboard Cite

The analog Hopfield neural network with time delay and random connections has been studied for its similarities in activity to human electroencephalogram and its usefulness in other areas of the applied sciences such as speech recognition, image analysis, and electrocardiogram modeling. Our goal here is to understand the mechanisms that affect the rhythmic activity in the neural network and how the addition of a Gaussian noise contributes to the network behavior. The neural network studied is composed of ten identical neurons. We investigated the excitatory and inhibitory networks with symmetric (square matrix) and asymmetric (triangular matrix) connections. The differential equations that model the network are solved numerically using the stochastic second-order Runge–Kutta method. Without noise, the neural networks with symmetric and asymmetric matrices possessed different synchronization properties: fully connected networks were synchronized both in time and in amplitude, while asymmetric networks were synchronized in time only. Saturation outputs of the excitatory neural networks do not depend on the time delay, whereas saturation oscillation amplitudes of inhibitory networks increase with the time delay until the steady state. The addition of the Gaussian noise is shown to significantly amplify small-amplitude oscillations, dramatically accelerates the rate of amplitude growth to saturation, and changes synchronization properties of the neural network outputs.

show abstract

Stochastic fixed-time synchronization for multilayer derivative dynamic Cohen-Grossberg networks via quantitative control

Tan

¹

,

Zhou

²

2022

Preprint

View full text Add to dashboard Cite

The implementation of fixed-time synchronization is a challenging problem for dynamic networks with derivative links. When there are derivative links in multilayer heterogeneous dynamic networks, it is difficult to obtain the fixedtime stable synchronization criteria via using the conventional Lyapunov function. So we choose a special Lyapunov function to solve the fixed-time stable synchronization criteria. In this paper, different from the comprehensive method used in lots of literature, to design and solve the fixed time controller, we use the analysis method to design a fixed time control strategy. When this strategy is used for the fixed-time synchronization of multilayer Heterogeneous networks with Cohen-Grossberg neural subnet, it will result in the designed controller does not contain differential terms, so as to reduce the difficulty in the design of fixed time controller. To be closer to reality, we consider multilayer neural networks with stochastic disturbances and nonlinear connections. When designing the controller, considering the actual communication constraints, we introduce quantization into the designed controller. Under the theoretical framework, we find that the upper limit for function of synchronization time is related to the quantization intensity, parameters of the designed Lyapunov function, parameters of the controller and a maximum eigenvalue related to the structure of multilayer Cohen-Grossberg neural networks. Finally, a simulation is supported to illustrate the effective of the derived theoretical framework.

show abstract

Synchronization, Multiresonance Phenomena, and Discrete Oscillation Periods in a Hopfield Neural Network with Two Time Delays

Cited by 3 publications

References 31 publications

Stochastic fixed-time quantitative synchronization for multilayer derivative dynamic Cohen–Grossberg networks and secure communication

Stochastic fixed-time quantitative synchronization for multilayer derivative dynamic Cohen–Grossberg networks and secure communication

Role of asymmetry and external noise in the development and synchronization of oscillations in the analog Hopfield neural networks with time delay

Stochastic fixed-time synchronization for multilayer derivative dynamic Cohen-Grossberg networks via quantitative control

Contact Info

Product

Resources

About