Study Of Nonlinear Dynamics Of Cyclic System Of Interacting Three Atoms

The physical world is full of complexity. Both the development of the natural things and inter-relationships between them are nonlinear. Some researches show that even simple nonlinear system can express complicated dynamic behaviors, which make the study of nonlinear especially important. In the present paper, we studied nonlinear dynamic behaviors of the cyclic system of interacting three atoms with two-energy-level. We want to reveal the possible modes of energy exchange of interacting three atoms, since we all know that the transportable mode of the energy and the electric charge is very important both in the molecular chain and in the application to physics, chemistry, biology, material, informatics, etc.In 1994, Zhu and Koyabashi showed that intrinsic self-localized Frenkel excitons can exist in a linear chain of interacting Frenkel excitons. This system may be taken as a model of energy transport in molecular or atomic chains. Based on the theory, we try to investigate the possible modes of energy exchange of interacting three atoms through the nonlinear dynamic method. Since nonlinear equations dissatisfy linear superposition principle, it is very difficult to solve the analytical solution. In this paper, we numerically simulate the dynamic process by using four-order Runge-Kutta algorithm. Meanwhile, in order to analyze the dynamic characteristics of this cyclic system accurately, we shall investigate the nonlinear equations by using Lyapunov exponent spectrum, bifurcation diagram, phase diagram, Poincare section and power spectrum.Through analyzing the cyclic system of interacting three atoms, this paper mainly covers the following work,Firstly, we calculated the dynamic behaviors of cyclic system with different initial values but the same system nonlinear coefficients. Meanwhile, a comparative analysis is given about their dynamic behaviors. Our results show when the initial values are changed, the amplitudes of three variables in the equations present irregular oscillation, the dynamics of the system has undergone great changes. This shows that the modes of energy exchange of interacting three atoms have great changes with the change of the initial values. Especially, when the system coefficients are very large, the modes of energy exchange are often irregular.Secondly, when the system initial values are different, the dynamics are calculated with keeping the nonlinear coefficientsμ=1 or 3 and varyingγor keepingγ=1 or 3 and varyingμ, respectively. Meanwhile, their dynamical characteristics are analyzed comparatively. Our results show that when nonlinear coefficients are changed, the dynamical behaviors of three variables in equations will take place irregular changes. This indicates that the modes of energy exchange will also have great changes. Especially when nonlinear coefficientγis fixed, and another nonlinear coefficientμis very small, the irregular change in behavior is weak, but whenμis increased gradually, the irregular behaviors will gradually take up the dominant position. This demonstrates that the modes of energy exchange of interacting three atoms are anomalous.