Analytical and Approximate Methods for Complex Dynamical Systems / edited by Alexander Timokha.

Format:

Book

Contributor:

Timokha, Alexander., Editor.

Series:

Understanding Complex Systems, 1860-0840

Language:

English

Subjects (All):

Dynamics.

Nonlinear theories.

System theory.

Engineering--Data processing.

Engineering.

Applied Dynamical Systems.

Complex Systems.

Data Engineering.

Local Subjects:

Applied Dynamical Systems.

Complex Systems.

Data Engineering.

Physical Description:

1 online resource (VIII, 378 p. 72 illus., 53 illus. in color.)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This book presents Analytical and Approximate Methods for Complex Dynamical Systems and introduces ideas of discontinuous mapping treated as complex dynamical systems. Mathematicians of world-recognized Ukrainian scientific schools established by M.Krylov, M.Bogolyubov, Yu.Mitropolskiy, and A.Sharkovsky used to cooperate for writing the collective book whose purpose consists of illustrating a synergy of combining diverse (by idea and technique) constructive analytical and approximate approaches and methods in complex dynamical systems which are herein associated with mathematical models of networks, conflict/economic theories, sloshing, soft matter, and even levitating drops. Readers are facilitated to learn contemporary insights, fundamentals (Parts I and III), applications (Part II), and components of theories of bifurcation, synchronization/self-organization, collective dynamics, chaos, solitons, fractional differential equations, symmetry, reduced order modelling, and many others, that makes the book useful for both graduate and postgraduate students, lecturers, researchers, and even engineers dealing with multidimensional dynamic systems.

Contents:

Part I: General and specific problems of complex dynamical systems

Organising centres in a 2D discontinuous map

Phase models for coupled oscillator networks

The conflict problem and opinion formation models

Dynamics of conflict interaction in terms of minimal players

Generalised intermittency in non-ideal and “classical” dynamical systems

Lanchester’s equations in conflicting sides using ODEINT Python library

Reversible saddle-node separatrix-loop bifurcation

Stationary and travelling synchronisation patterns in systems of coupled active rotators

Part II: Continuum media modelling

Complex dynamical systems of two-dimensional sloshing in rectangular tank

Swirling-type sloshing in square base tank due to orbital excitations

Towards kinetic equations of open systems of active soft matter

Freely oscillating drop

Nonlinear WKB method, asymptotic soliton-like solutions of variable coefficients Korteweg–de Vries equations with singular perturbation and Rankine–Hugoniot-type conditions

Part III: Auxiliary problems of complex dynamical systems

On group classification of nonlinear heat equation: algebraic approach

Mathematical modelling of the interconnected boundary-value problems in the Hilbert space

Averaging in a generalised multifrequency system with a delay

Exponentially convergent method for Hardy-Titchmarsh–type equation with unbounded operator coefficient in Banach space

Regularization of linear impulsive boundary value problem for systems of integro-differential equations

Interconnected system for the Lyapunov equation with control and boundary conditions

Lyapunov function and smooth periodic solutions to quasilinear 1D hyperbolic systems.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783031773785

3031773780

OCLC:

1524424111