Information Geometry of Nonlinear Stochastic Systems

Nonlinear Vibration Analysis of a cantilever beam with nonlinear geometry

Analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. According to this, an impressive analytical method which is called Modified Iteration Perturbation Method (MIPM) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. This new method is combined by the Mickens and Iteration methods. Moreover, this method don...

Dynamics of Nonlinear Stochastic Systems

Stochastic Controllability of Nonlinear Systems

In the paper stochastic dynamical control systems described by nonlinear stationary ordinary differential state equations are considered. Using a generalized open mapping theorem, sufficient conditions for constrained local stochastic controllability in a given time interval are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed con...

Information geometry on complexity and stochastic interaction

Stochastic Reasoning, Free Energy, and Information Geometry

Belief propagation (BP) is a universal method of stochastic reasoning. It gives exact inference for stochastic models with tree interactions and works surprisingly well even if the models have loopy interactions. Its performance has been analyzed separately in many fields, such as AI, statistical physics, information theory, and information geometry. This article gives a unified framework for u...