Abstract：Empirical and theoretical investigations of chaotic phenomena in macroeconomic systems are presented. Basic issues and techniques in testing economic aggregate movements are discussed. Evidence of low dimensional strange attractors is found in several empirical monetary aggregates. A continuous time deterministic model with delayed feedback is proposed to describe the monetary growth. Phase transition from periodic to chaotic motion occurs in the model. The model offers an explanation of the multiperiodicity and irregularity in business cycles and of the low-dimensionality of chaotic monetary attractors. Implications in monetary control policy and a new approach to forecasting business cycles are suggested.
Chen, Ping. “Empirical and theoretical evidence of economic chaos,” System Dynamics Review, Vol. 4, No. 1-2, 81-108 (1988). Also, in Chen (2010) Chapter 4, pp.85-113.
Abstract: Nonlinear models are introduced to describe the nonequilibrium dynamics of social evolution. The difference between Western and Oriental culture, and their roles in the origin in the division of labor, are described by a behavioral model in information diffusion and learning competition. It shows a trade-off between stability and diversity. The stochastic mechanism of social differentiation and the empirical evidence for this is discussed in a stochastic model of multistaged development. It shows that the break-down of the Gaussian distribution during a transition. Finally, an ideal model of social bifurcation is given.
Key Words: Information diffusion, learning, competition, behavior, division of labor, bifurcation
“Origin of Division of Labor and Stochastic Mechanism of Differentiation,” European Journal of Operational Research, Vol. 30, No. 3, pp. 246-250 (1987). Also, in Chen (2010), Chapter 8, pp.201-209.
There are two important laws of transitivity in physics (Zhao, 1991).One is the zeroth law of thermodynamics, which states the transitivity of thermal equilibrium. The other is the law of the transitivity of simultaneity in general relativity (Landau and Lifshitz, 1975), which says that one can synchronize coordinate clocks placed along a closed path to a simultaneous moment if and only if the reference frame is time-orthogonal.In this paper, we will give a fundamental and intrinsic relationship between the two laws on transitivity in physics. The transitivity of thermal equilibrium is equivalent to the transitivity of clock rate synchronization.In Section 2 we show the relationship between the transitivity of thermal equilibrium and the transitivity of clock rate synchronization by means of the thermal Green function. In Section 3 we discuss “clock synchronization” and “clock rate synchronization” in general relativity, and give a condition on “clock rate synchronization” which is different from that given by Landau and Lifshitz. We present a conclusion and discussion in Section 4.
Zhao Zheng & Ping Chen “Zeroth Law of Thermodynamics and Transitivity of Simultaneity,” International Journal of Theoretical Physics, 36(10), 2153-2159 (1997).
