Dynamical System in Chaotic Neurons with Time Delay Self-Feedback and Its Application in Color Image Encryption

Noise is ubiquitous in the real-world environment. At present, most scholars only include the stage of Gaussian white noise when applying noise in neural networks and regard white noise as a tool to optimize the network model, which is far from enough, because noise not only affects the optimization ability of the Hopfield neural network but can also better fit the needs of the actual use of the scene. Therefore, according to the problems in the existing research, a method is proposed to combine the neural network with colored noise according to the signal-to-noise ratio. Taking blue noise as an example, the anti-interference ability of the Hopfield neural network regarding colored noise is studied. The results show that for the Hopfield neural network driven by blue noise, by adjusting the neural network step size, excitation function and signal-to-noise ratio, it not only provides ideas for adding colored noise to the neural network but also enables the neural network model to have better optimization-seeking ability. The research results have some reference significance for improving the practical application of neural networks in noisy environments.

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Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling

Qiao

Liang

Tavares

et al. 2023

Entropy

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Chaotic time series are widely present in practice, but due to their characteristics—such as internal randomness, nonlinearity, and long-term unpredictability—it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.

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Dynamical System in Chaotic Neurons with Time Delay Self-Feedback and Its Application in Color Image Encryption

Cited by 3 publications

References 58 publications

Stochastic Morris–Lecar model with time delay under magnetic field excitation

Stochastic Morris–Lecar model with time delay under magnetic field excitation

The Effect of Blue Noise on the Optimization Ability of Hopfield Neural Network

Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling

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