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 equations with delays. This work continues and
complements the author's previous book Lyapunov Functionals and
Stability of Stochastic Difference Equations, where this method is
described for difference equations with discrete and continuous time.
The text begins with both a description and a delineation of the
peculiarities of deterministic and stochastic functional differential
equations. There follows basic definitions for stability theory of
stochastic hereditary systems, and the formal procedure of Lyapunov
functionals construction is presented. Stability investigation is
conducted for stochastic linear and nonlinear differential equations
with constant and distributed delays. The proposed method is used for
stability investigation of different mathematical models such as: -
inverted controlled pendulum; - Nicholson's blowflies equation; -
predator-prey relationships; - epidemic development; and - mathematical
models that describe human behaviours related to addictions and obesity.
Lyapunov Functionals and Stability of Stochastic Functional Differential
Equations is primarily addressed to experts in stability theory but will
also be of interest to professionals and students in pure and
computational mathematics, physics, engineering, medicine, and biology.
