The phenomenon of stochastic resonance (SR) in a second-order and underdamped asymmetric bistable system is investigated. The second-order asymmetric bistable system with Gauss white noise is stochastically equivalent to two-dimensional Markovian process, and the exact expression of the signal-to-noise ratio (SNR) of system response in the presence of weak periodic driving force is obtained under the adiabatic condition and the theory of two-state model intensities. The influences of the damping parameter, asymmetry constant r and the Gaussian white noises on the SNR are discussed. The present calculation results show that, the increase of static asymmetry r and damping parameter γ can restrain the SR phenomenon appears. However, the increase of signal amplitude A can enhance SR.
In this paper, we propose a new integral global optimization algorithm for finding the solution of continuous minimization problem, and prove the asymptotic convergence of this algorithm. In our modified method we use variable measure integral, importance sampling and main idea of the cross-entropy method to ensure its convergence and efficiency. Numerical results show that the new method is very efficient in some challenging continuous global optimization problems.
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