Chaotic behavior in differential equations driven by a Brownian motion
The authors examine the chaotic behaviour exhibited by ordinary differential equations having a homoclinic orbit to a saddle point under unbounded random forcing driven by Brownian motion. The approach is `sample-wise', though the need for using the features of the Brownian motion as a whole is noted. Application is made to the Duffing equation and the non-linear pendulum.
scientific article; zbMATH DE number 5957028
scientific article