Stability of stochastic impulsive differential equations: integrating the cyber and the physical of stochastic systems.

According to Newton's second law of motion, we humans describe a dynamical system with a differential equation, which is naturally discretized into a difference equation whenever a computer is used. The differential equation is the continuous-time model in human brains and the difference equation the disceret-time model in computers for the dynamical system. This paper formulates a hybrid model with impulsive differential equations for the dynamical system, which integrates its continuous-time model in human brains and its discrete-time counterpart in computers. The presented results establish a theoretic foundation for the scientific study of control and communication in the animal/human and the machine (Norbert Wiener) in the era of rise of the machines.