With both additive and multiplicative noise excitations,the effect on the chaotic behaviour of the dynamical system is investigated in this paper.The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos.As an example,for the Duffing system,we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos,and by combining figures,we discuss the influences of the amplitude,intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately.Finally,numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincar map.
In this paper, based on the invariance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node's state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.
Investigations of low energy transfer trajectories are important for both celestial mechanics and astronautics. Methodologies using the theories from dynamical systems are developed in recent years. This paper investigates the dynamics of the eartah-moon system. Low energy transfer trajectories are solved numerically by employing a hybrid strategy: first, a genetic hide and seek method performs a search in large domain to confine the global minimum f (η) (objective function) region; then, a deterministic Nelder-Mead method is utilized to refine the minimum quickly. Some transfer trajectories of the spacecraft in the earth-moon system are successfully simulated which verify the desired efficiency and robustness of the method of this paper.
This paper investigates the stochastic resonance(SR) phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured.The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system.Moreover,the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon,while the cross-correlation time τ can strengthen the SR phenomenon.
