Analysis of stochastic bifurcation and chaos in stochastic Duffing–van der Pol system via Chebyshev polynomial approximation

2006 ◽  
Vol 15 (6) ◽  
pp. 1231-1238 ◽  
Author(s):  
Ma Shao-Juan ◽  
Xu Wei ◽  
Li Wei ◽  
Fang Tong
Keyword(s):  
Chebyshev Polynomial ◽  
Polynomial Approximation ◽  
Stochastic Bifurcation ◽  
Van Der Pol ◽  
Bifurcation And Chaos ◽  
Chebyshev Polynomial Approximation

scholarly journals Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Hua Dong ◽  
Xianghua Zhao
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Chebyshev Polynomial ◽  
Polynomial Approximation ◽  
Risk Model ◽  
Arbitrary Distribution ◽  
System Of Differential Equations ◽  
Numerical Result ◽  
Chebyshev Polynomial Approximation ◽  
Markov Modulated

This paper considers a perturbed Markov-modulated risk model with two-sided jumps, where both the upward and downward jumps follow arbitrary distribution. We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. Finally, an example is provided to illustrate the method.

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