Dynamics of asymmetric kinetic Ising systems revisited

Abstract

The dynamics of an asymmetric kinetic Ising model is studied. Two schemes for improving the existing mean-field description are proposed. In the first scheme, we derive the formulas for instantaneous magnetization, equal-time correlation, and time-delayed correlation, considering the correlation between different local fields. To derive the time-delayed correlation, we emphasize that the small correlation assumption adopted in previous work [M. Mézard and J. Sakellariou, J. Stat. Mech., L07001 (2011)] is in fact not required. To confirm the inference efficiency of our method, we perform extensive simulations on single instances with either temporally constant external driving fields or sinusoidal external fields. In the second scheme, we develop an improved mean-field theory for instantaneous magnetization prediction utilizing the notion of the cavity system in conjunction with a perturbative expansion approach. Its efficiency is numerically confirmed by comparison with the existing mean-field theory when partially asymmetric couplings are present.

16 pages, 5 figures, Journal of Statistical Mechanics: Theory and Experiment (in press)

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• On the number of limit cycles in diluted neural networks
• Structure of attractors in randomly connected networks
• Freezing chaos without synaptic plasticity