【摘要】 从力学角度,将一种三维非线性金融系统分解成Kolmogorov系统的保守力矩、耗散力矩以及外力矩,并分析不同力矩作用于该金融系统时的动态特性,剖析该金融系统产生混沌行为的原因,并结合金融市场解释其物理意义。为控制该金融系统的混沌行为,基于有限时间的LaSalle不变集理论,设计一种自适应控制器。理论分析和数值仿真表明,此控制器作用于系统时会在有限时间内有效地将混沌的金融系统控制到稳定状态。更多还原

【Abstract】 The mechanical analysis and chaos control of a three-dimensional(3D)nonlinear financial system are investigated in this paper. Based on the formalism of the Kolmogorov system,the financial system can be divided into three parts:conservative torque,dissipative torque,and exterior torque. The dynamical behaviors of different torques introduced into the 3D financial system are discussed numerically and the mechanism of the occurrence of chaos is uncovered. Then,its physical meaning of the interaction effect of different state variables is explained. To control the chaotic dynamics of the 3D system,an adaptive control scheme is designed to suppress chaos based on the finite time LaSalle invariant set theory. Theoretical analysis and numerical results show that the proposed control scheme is effective for controlling the 3D chaotic financial system to a stable state.更多还原