Focusing on the problem of solving coupled Logistic fractional-order differential equation, a discretization method was introduced to solve it discretly. Firstly, a coupled Logistic integer-order differential equation was introduced into the fields of fractional-order calculus. Secondly, the corresponding coupled Logistic fractional-order differential equation with piecewise constant arguments was analyzed and the proposed discretization method was applied to solve the model numerically. Then, according to the fixed point theory, the stability of the fixed point of the synthetic dynamic system was discussed, and the boundary equation of the first bifurcation of the coupled Logistic fractional-order system in the parameter space was given. Finally, the model was numerically simulated by Matlab, and more complex dynamics phenomena of model were discussed with Lyapunov index, phase diagram, time series diagram and bifurcation diagram. The simulation results show that, the proposed method is successful in discretizing coupled Logistic fractional-order differential equation.

In order to estimate the State-Of-Charge (SOC) of automobile power lithium-ion battery online, an Unscented Kalman Filtering (UKF) algorithm was proposed combined with neural network. First of all, Thevenin circuit was treated as an equivalent circuit, the state space representation of the battery model was established and the least square method was applied to identify the parameters of model. Then on this basis, the neural network algorithm was expected to fit the functional relationships between SOC of battery and model parameters respectively. After many experiments, the convergence curve of the neural network algorithm was determined. The proposed method was more accurate than the traditional curve fitting. In addition, the Extended Kalman Filtering (EKF) principle and the UKF principle were introduced separately and some tests were designed including the validation experiment of battery equivalent circuit model, the test experiment of SOC and the convergence experiment of the algorithms. The experimental results show that, the proposed method which can be used for SOC estimation online has higher estimation precision and stronger environmental adaptability than simple extended Kalman filtering algorithm under different conditions, its maximum error is less than 4%. Finally, the proposed algorithm combining UKF and neural network has better convergence and robustness, which can be used to solve the problems of inaccurate estimation of initial value and cumulative error effectively.