论文信息 - On the probability of chaos in large dynamical systems: A Monte Carlo study

On the probability of chaos in large dynamical systems: A Monte Carlo study

Abstract In this paper we report the result of a Monte Carlo study on the probability of chaos in large dynamical systems. We use neural networks as the basis functions for the system dynamics and choose parameter values for the networks randomly. Our results show that as the dimension of the system and the complexity of the network increase, the probability of chaotic dynamics increases to 100%. Since neural networks are dense in the set of dynamical systems, our conclusion is that most large systems are chaotic.

[1] Julien Clinton Sprott,et al. How common is chaos , 1993 .

[2] Gerhard Sorger. Minimum impatience theorems for recursive economic models , 1992 .

[3] B. Cessac,et al. CONTROL OF THE TRANSITION TO CHAOS IN NEURAL NETWORKS WITH RANDOM CONNECTIVITY , 1993 .

[4] W. Brock. PATHWAYS TO RANDOMNESS IN THE ECONOMY , 1993 .

[5] F. Takens. Detecting strange attractors in turbulence , 1981 .

[6] Kurt Hornik,et al. Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[7] Halbert White,et al. Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings , 1990, Neural Networks.

[8] Kurt Hornik,et al. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks , 1990, Neural Networks.

[9] Pierre L'Ecuyer,et al. Efficient and portable combined random number generators , 1988, CACM.

[10] William H. Press,et al. Numerical Recipes in C, 2nd Edition , 1992 .

[11] L. Montrucchio,et al. On the indeterminacy of capital accumulation paths , 1986 .