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In this paper, three modified Lesile-Gower predator-prey models with two time delays are considered. Taking the time delay as bifurcation parameter, when Hopf bifurcation occurs, the critical value corresponding to time delay is obtained. By using normal form theory and central manifold argument, the direction of Hopf bifurcation and the stability of bifurcation periodic solution can be determined. Finally, numerical simulation is performed to support theoretical analysis.

Steering control for autonomous vehicles is used for more complex scenarios, such as nonlinear scenarios and varied vehicle speeds scenarios during the actual driving process. Model Predictive Control (MPC) is known as a feasible method for multi-constraints. However, a complicated mathematical model will lead to a great computational burden. To deal with this issue, a modified MPC-based adaptive steering strategy with nonlinear compensation by using Double Deep Q-learning Network Algorithm (DDQN) is proposed. Considering the real-time requirement for steering control, MPC is used as a basic controller to calculate the linear turning case. Then a DDQN algorithm is applied for compensating the errors caused by the nonlinear feature of the vehicle and the time-varying speed. Finally, numerical validations and experimental tests in a real vehicle are conducted to verify the effectiveness of the proposed control strategy. The traditional MPC and only the DDQN method are applied as the benchmark strategies. The comparison validation results under different speed and vehicle parameters indicate that the proposed method has superior performance in adapting to time-varying speeds and vehicle nonlinear features. And the experimental tests based on actual driving scenarios also validate the remarkable stability of the developed control method.