We find that incorporating nonlinearities into tests of asset price bubbles has important consequences for the results. We show this by comparing four tests using S&P 500 data. Our results indicate that the modi fication which incorporates nonlinear probabilities outperforms the other models in...

The control of gyroscope system is a trivial problem where in the three degree of freedom is coupled to make the system nonlinear. This paper attempt to design of control algorithm without the usage Lyapunov exponent and also effective in handling the nonlinear terms associated in the dynamics...