A novel fractional-order memristive Hopfield neural network for traveling salesman problem and its FPGA implementation

This paper proposes a novel fractional-order memristive Hopfield neural network (HNN) to address traveling salesman problem (TSP). Fractional-order memristive HNN can efficiently converge to a globally optimal solution, while conventional HNN tends to become stuck at a local minimum in solving TSP. Incorporating fractional-order calculus and memristors gives the system long-term memory properties and complex chaotic characteristics, resulting in faster convergence speeds and shorter average distances in solving TSP. Moreover, a novel chaotic optimization algorithm based on fractional-order memristive HNN is designed for the calculation process to deal with mutual constraint between convergence accuracy and convergence speed, which circumvents random search and diminishes the rate of invalid solutions. Numerical simulations demonstrate the effectiveness and merits of the proposed algorithm. Furthermore, Field Programmable Gate Array (FPGA) technology is utilized to implement the proposed neural network.

Bogdanov-Takens singularity in tri-neuron network with time delay

This brief reports a retarded functional differential equation modeling tri-neuron network with time delay. The Bogdanov-Takens (B-T) bifurcation is investigated by using the center manifold reduction and the normal form method. We get the versal unfolding of the norm forms at the B-T singularity and show that the model can exhibit pitchfork, Hopf, homoclinic, and double-limit cycles bifurcations. Some numerical simulations are given to support the analytic results and explore chaotic dynamics. Finally, an algorithm is given to show that chaotic tri-neuron networks can be used for encrypting a color image.

Noise-tuning-based hysteretic noisy chaotic neural network for broadcast scheduling problem in wireless multihop networks

Compared with noisy chaotic neural networks (NCNNs), hysteretic noisy chaotic neural networks (HNCNNs) are more likely to exhibit better optimization performance at higher noise levels, but behave worse at lower noise levels. In order to improve the optimization performance of HNCNNs, this paper presents a novel noise-tuning-based hysteretic noisy chaotic neural network (NHNCNN). Using a noise tuning factor to modulate the level of stochastic noises, the proposed NHNCNN not only balances stochastic wandering and chaotic searching, but also exhibits stronger hysteretic dynamics, thereby improving the optimization performance at both lower and higher noise levels. The aim of the broadcast scheduling problem (BSP) in wireless multihop networks (WMNs) is to design an optimal time-division multiple-access frame structure with minimal frame length and maximal channel utilization. A gradual NHNCNN (G-NHNCNN), which combines the NHNCNN with the gradual expansion scheme, is applied to solve BSP in WMNs to demonstrate the performance of the NHNCNN. Simulation results show that the proposed NHNCNN has a larger probability of finding better solutions compared to both the NCNN and the HNCNN regardless of whether noise amplitudes are lower or higher.