Abstract
This paper studies a simple dynamical system of stock price fluctuation time series based on the rule of stock market. When the stock price fluctuation system is disturbed by external excitations, the system exhibits obviously chaotic phenomena, and its basic dynamic properties are analyzed. At the same time, a new fixed‐time convergence theorem is proposed for achieving fixed‐time control of stock price fluctuation system. Finally, the effectiveness of the method is verified by numerical simulation.
Highlights
This paper studies a simple dynamical system of stock price fluctuation time series based on the rule of stock market
Since Lorenz found the first chaotic attractor [1], a variety of chaotic systems have been found, and in particular chaotic phenomenon appeared in the economic system; for example, Chen discovered the existence of chaotic attractor in stock market [2]
This paper attempts to propose a new finite time convergence theory to discuss the control problem of stock price fluctuation system, the new fixed-time stability method proposed in this paper converged faster than the proposed method by Zuo, and the new fixed-time stable theorem contains the theorem proposed by Zuo, so the new fixed-time stable theorem can be applied more widely
Summary
Since Lorenz found the first chaotic attractor [1], a variety of chaotic systems have been found, and in particular chaotic phenomenon appeared in the economic system; for example, Chen discovered the existence of chaotic attractor in stock market [2]. The nonlinear phenomenon of price fluctuation and the external excitations of the dynamic system [10] are common in practice. This paper attempts to propose a new finite time convergence theory to discuss the control problem of stock price fluctuation system, the new fixed-time stability method proposed in this paper converged faster than the proposed method by Zuo, and the new fixed-time stable theorem contains the theorem proposed by Zuo, so the new fixed-time stable theorem can be applied more widely. The main contributions of this paper are as follows: (1) a stock price fluctuation dynamical system is established under the influence of external excitations, and its basic dynamic behavior is analyzed. (3) According to the new fixed-time convergence theorem, the fixed-time control criterion of the stock price fluctuation dynamical system is given The main contributions of this paper are as follows: (1) a stock price fluctuation dynamical system is established under the influence of external excitations, and its basic dynamic behavior is analyzed. (2) A new fixedtime convergence theorem is proposed. (3) According to the new fixed-time convergence theorem, the fixed-time control criterion of the stock price fluctuation dynamical system is given
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