Based on the four non-linear system models, the neural network structure identification of a typical unstable, non-linear and strong coupling inverted pendulum system is established.

The presence of homoclinic tangencies and homoclinic intersection makes it difficult if not impossible,to denoise or shadow the trajectory of a non-hyperbolic nonlinear system.

Timoshenko beam model is considered to solve dynamic characteristics and unbalanced response of a rotor system with a flexible shaft and rigid disks supported by non-conservative flexible bearings using a technique called the generalized polynomial expansion method(GPEM).