東華大學圖書館 |

Analytical and approximate methods for complex dynamical systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analytical and approximate methods for complex dynamical systems/ edited by Alexander Timokha.
other author:	Timokha, Alexander.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	viii, 378 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Differentiable dynamical systems. -
Online resource:	https://doi.org/10.1007/978-3-031-77378-5
ISBN:	9783031773785

Analytical and approximate methods for complex dynamical systems
Analytical and approximate methods for complex dynamical systems[electronic resource] /edited by Alexander Timokha. - Cham :Springer Nature Switzerland :2025. - viii, 378 p. :ill. (some col.), digital ;24 cm. - Understanding complex systems,1860-0840. - Understanding complex systems..

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.

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.

ISBN: 9783031773785

Standard No.: 10.1007/978-3-031-77378-5doiSubjects--Topical Terms:

524351
Differentiable dynamical systems.

LC Class. No.: QA614.8

Dewey Class. No.: 515.39

Analytical and approximate methods for complex dynamical systems
LDR:03999nmm a2200361 a 4500 001 2409129
003 DE-He213
005 20250316141048.0
006 m d
007 cr nn 008maaau
008 260204s2025 sz s 0 eng d
020 $a 9783031773785 $q (electronic bk.)
020 $a 9783031773778 $q (paper)
024 7 $a 10.1007/978-3-031-77378-5 $2 doi
035 $a 978-3-031-77378-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA614.8
072 7 $a TBJ $2 bicssc
072 7 $a GPFC $2 bicssc
072 7 $a SCI064000 $2 bisacsh
072 7 $a TBJ $2 thema
072 7 $a GPFC $2 thema
082 0 4 $a 515.39 $2 23
090 $a QA614.8 $b .A532 2025
245 0 0 $a Analytical and approximate methods for complex dynamical systems $h [electronic resource] / $c edited by Alexander Timokha.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a viii, 378 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Understanding complex systems, $x 1860-0840
505 0 $a 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.
520 $a 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.
650 0 $a Differentiable dynamical systems. $3 524351
650 1 4 $a Applied Dynamical Systems. $3 3538870
650 2 4 $a Complex Systems. $3 1566441
650 2 4 $a Data Engineering. $3 3409361
700 1 $a Timokha, Alexander. $3 3782143
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Understanding complex systems. $3 1568162
856 4 0 $u https://doi.org/10.1007/978-3-031-77378-5
950 $a Engineering (SpringerNature-11647)