The Effect of Colored Noise on Self-feedback Chaotic Neural Networks with Legendre Function

In the real world, any network model will inevitably be affected by noise. As a result, the academic community has gradually started to pay attention to various types of complex systems based on colored noise, but the application of colored noise to neural networks is still a blank field. The introduction of colored noise can make the operation of neural networks closer to the real application scenarios and avoid errors. Therefore, this article introduces four typical colored noises into Legendre function self-feedback chaotic neural networks, which are used to analyze the effects of colored noise on neural network models, and gives the maximum Lyapunov exponent and single neuron inverse bifurcation diagram of the network with colored noise. The Legendre function self-feedback chaotic neural network with colored noise is applied to solve the 10-city travelers problem. Simulation studies indicate that: with appropriate parameters, the Legendre function self-feedback chaotic neural network maintains excellent solution performance under colored noise interference at any signal-to-noise ratio, and the network model speeds up convergence due to noise interference on the basis of improved accuracy of the optimization algorithm. The findings provide theoretical support for the hardware implementation of this neural network in a realistic environment.