Mathematics of Continuous and Discrete Dynamical Systems: Contemporary Mathematics

Included are papers
on design and analysis of discrete-time and continuous-time dynamical
systems arising in the natural and engineering sciences, in particular,
the design of robust nonstandard finite-difference methods for solving
continuous-time ordinary and partial differential equation models,
the analytical and numerical study of models that undergo nonlinear
oscillations, as well as the design of deterministic and stochastic
models for epidemiological and ecological processes. Some of the
specific topics covered in the book include the analysis of
deterministic and stochastic SIR-type models, the assessment of
cost-effectiveness of vaccination problems, finite-difference methods
for oscillatory dynamical systems (including the Schrödinger equation
and Brusselator system), the design of exact and elementary stable
finite-difference methods, the study of a two-patch model with Allee
effects and disease-modified fitness, the study of the delay
differential equation model with application to circadian rhythm and
the application of some special functions in the solutions of some
problems arising in the natural and engineering sciences.

A
notable feature of the book is the collection of some relevant open
problems, intended to help guide the direction of future research in
the area.