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This book develops analytical methods for studying the dynamical
chaos, synchronization, and dynamics of structures in various
models of coupled rotators. Rotators and their systems are defined
in a cylindrical phase space, and, unlike oscillators, which are
defined in Rn, they have a wider "range" of motion: There are
vibrational and rotational types for cyclic variables, as well as
their combinations (rotational-vibrational) if the number of cyclic
variables is more than one. The specificity of rotator phase space
poses serious challenges in terms of selecting methods for studying
the dynamics of related systems. The book chiefly focuses on
developing a modified form of the method of averaging, which can be
used to study the dynamics of rotators. In general, the book uses
the "language" of the qualitative theory of differential equations,
point mappings, and the theory of bifurcations, which helps authors
to obtain new results on dynamical chaos in systems with few
degrees of freedom. In addition, a special section is devoted to
the study and classification of dynamic structures that can occur
in systems with a large number of interconnected objects, i.e. in
lattices of rotators and/or oscillators. Given its scope and
format, the book can be used both in lectures and courses on
nonlinear dynamics, and in specialized courses on the development
and operation of relevant systems that can be represented by a
large number of various practical systems: interconnected grids of
various mechanical systems, various types of networks including not
only mechanical but also biological systems, etc.
This book develops analytical methods for studying the dynamical
chaos, synchronization, and dynamics of structures in various
models of coupled rotators. Rotators and their systems are defined
in a cylindrical phase space, and, unlike oscillators, which are
defined in Rn, they have a wider "range" of motion: There are
vibrational and rotational types for cyclic variables, as well as
their combinations (rotational-vibrational) if the number of cyclic
variables is more than one. The specificity of rotator phase space
poses serious challenges in terms of selecting methods for studying
the dynamics of related systems. The book chiefly focuses on
developing a modified form of the method of averaging, which can be
used to study the dynamics of rotators. In general, the book uses
the "language" of the qualitative theory of differential equations,
point mappings, and the theory of bifurcations, which helps authors
to obtain new results on dynamical chaos in systems with few
degrees of freedom. In addition, a special section is devoted to
the study and classification of dynamic structures that can occur
in systems with a large number of interconnected objects, i.e. in
lattices of rotators and/or oscillators. Given its scope and
format, the book can be used both in lectures and courses on
nonlinear dynamics, and in specialized courses on the development
and operation of relevant systems that can be represented by a
large number of various practical systems: interconnected grids of
various mechanical systems, various types of networks including not
only mechanical but also biological systems, etc.
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