Lyapunov Functionals and Stability of Stochastic Functional Differential Equations

• Main Author: Shaikhet, Leonid. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Heidelberg : Springer International Publishing : Imprint: Springer, 2013.
• Subjects: Engineering.; Functional equations.; Mathematical optimization.; Distribution (Probability theory).; Vibration.; Control.; Difference and Functional Equations.; Statistical Physics, Dynamical Systems and Complexity.; Calculus of Variations and Optimal Control; Optimization.; Probability Theory and Stochastic Processes.; Vibration, Dynamical Systems, Control.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-00101-2

Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential...

Table of Contents:

• Short Introduction to Stability Theory of Deterministic Functional Differential Equations
• Stability of Linear Scalar Equations
• Stability of Linear Systems of Two Equations
• Stability of Systems with Nonlinearities
• Matrix Riccati Equations in Stability of Linear Stochastic Differential Equations with Delays
• Stochastic Systems with Markovian Switching
• Stabilization of the Controlled Inverted Pendulum by Control with Delay
• Stability of Equilibrium Points of Nicholsons Blowflies Equation with Stochastic Perturbations
• Stability of Positive Equilibrium Point of Nonlinear System of Type of Predator-Prey with Aftereffect and Stochastic Perturbations
• Stability of SIR Epidemic Model Equilibrium Points
• Stability of Some Social Mathematical Models with Delay by Stochastic Perturbations.