Chaos in Hopfield Neural Network with Nonlinear Membrane Resistance and Its Application in Robot Path Planning

Recent studies have shown growing interest in chaotic dynamics in Hopfield Neural Networks (HNNs). While conventional HNN models use linear resistors to simulate neuronal membrane resistance, biological evidence suggests that membrane resistance exhibits nonlinear characteristics. To address this, we propose a novel HNN model incorporating nonlinear membrane resistance. We analyze its dynamical behavior through equilibrium stability and Hamiltonian energy analysis, and multiple numerical simulation methods. Furthermore, we apply the generated chaotic sequences to particle swarm optimization-based robot path planning, demonstrating its effectiveness in obstacle avoidance task.