In Chap. 5 stability of the zero solution and positive equilibrium points for nonlinear systems is studied. In particular, differential equations with nonlinearities in deterministic and stochastic parts are considered, differential equation with fractional nonlinearity. It is shown that investigation of stability in probability for nonlinear systems with the level of nonlinearity higher than one can be reduced to investigation of asymptotic mean square stability of the linear part of the considered nonlinear system. The obtained results are illustrated by 18 figures.


Equilibrium Point Trivial Solution Nonlinear Differential Equation Initial Function Stochastic Perturbation 
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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Leonid Shaikhet
    • 1
  1. 1.Department of Higher MathematicsDonetsk State University of ManagementDonetskUkraine

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