Ermakov–Ray–Reid systems with additive noise

• Euler–Maruyama numerical scheme with additive noise displayed for Ermakov systems.
• Ermakov–Lewis invariant is found less robust than in the case of multiplicative noise.
• Similar results are obtained for a more general Ermakov–Ray–Reid system.

Using the methods developed by us in Cervantes-López et al. (2014) for multiplicative noises, we present results on the effects of the additive noise on the Ermakov–Lewis invariant. This case can be implemented in the Euler–Maruyama numerical method if the additive noise is considered as the forcing term of the parametric oscillator and presented as a particular case of the Ermakov–Ray–Reid systems. The results are obtained for the same particular examples as for the multiplicative noise and show a tendency to less robustness of the Ermakov–Lewis invariant to the additive noise as compared to the multiplicative noise.