World Scientific Series On Nonlinear Science Series A: Integral Dynamical Models: Singularities, Signals And Control (ePub)

This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis.Contents:


Introduction and Overview

Volterra Models of Evolving Dynamical Systems:

Volterra Equations of the First Kind with Piecewise Continuous Kernels
Volterra Matrix Equation of the First Kind with Piecewise Continuous Kernels
Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels
Generalized Solutions to the Volterra Equations with Piecewise Continuous Kernels and Sources

Nonlinear Models, Singularities and Control:

Nonlinear Hammerstein Integral Equations
Nonlinear Volterra Operator Equations with Non-invertible Operator
Nonlinear Differential Equations Near Branching Points
Convex Majorants Method in the Theory of Nonlinear Volterra Equations
Generalized Solutions to Nonlinear Volterra Equations of the First Kind
On Impulse Control of Nonlinear Dynamical Systems Based on the Volterra Series

Integral Models Applications:

The Volterra Models Applications
Suppression of Moiré Patterns for Video Archive Restoration
Integral Models Applications in Electric Power EngineeringGraduate students and researchers in complex systems, mathematical modeling and machine learning.Key Features:


New unified view on integral models, bifurcation theory and behavioral modeling
Novel class of weakly regular Volterra equations is proposed, new approach to forecasting of power systems parameters