Nonlinear Dynamics, Chaos, and Complexity: In Memory of Professor Valentin Afraimovich

204 Pages·2021·6.915 MB·English

by  Dimitri Volchenkov

Nonlinear Physical Science
Dimitri Volchenkov   Editor
Nonlinear
Dynamics,
Chaos, and
Complexity
In Memory of Professor
Valentin Afraimovich
Nonlinear Physical Science
Series Editors
Albert C. J. Luo , Department of Mechanical and Industrial Engineering,
Southern Illinois University Edwardsville, Edwardsville, IL, USA
Dimitri Volchenkov , Department of Mathematics and Statistics, Texas Tech
University, Lubbock, TX, USA
Advisory Editors
Eugenio Aulisa , Department of Mathematics and Statistics, Texas Tech
University, Lubbock, TX, USA
Jan Awrejcewicz , Department of Automation, Biomechanics and Mechatronics,
Lodz University of Technology, Lodz, Poland
EugeneBenilov ,DepartmentofMathematics,UniversityofLimerick,Limerick,
Limerick, Ireland
Maurice Courbage, CNRS UMR 7057, Universite Paris Diderot, Paris 7, Paris,
France
DmitryV.Kovalevsky ,ClimateServiceCenterGermany(GERICS),Helmholtz‐
Zentrum Geesthacht, Hamburg, Germany
NikolayV.Kuznetsov ,FacultyofMathematicsandMechanics,SaintPetersburg
State University, Saint Petersburg, Russia
Stefano Lenci , Department of Civil and Building Engineering and Architecture
(DICEA), Polytechnic University of Marche, Ancona, Italy
Xavier Leoncini, Case321, Centre dePhysique Théorique,MARSEILLE CEDEX
09, France
EdsonDenisLeonel ,DepartmamentodeFísica,SaoPauloStateUniversity,Rio
Claro, São Paulo, Brazil
MarcLeonetti,LaboratoireRhéologieetProcédés,GrenobleCedex9,Isère,France
ShijunLiao,SchoolofNavalArchitecture,OceanandCivilEngineering,Shanghai
Jiao Tong University, Shanghai, China
Josep J. Masdemont , Department of Mathematics, Universitat Politècnica de
Catalunya, Barcelona, Spain
Dmitry E. Pelinovsky , Department of Mathematics and Statistics, McMaster
University, Hamilton, ON, Canada
Sergey V. Prants , Pacific Oceanological Inst. of the RAS, Laboratory of
Nonlinear Dynamical System, Vladivostok, Russia
Laurent Raymond , Centre de Physique Théorique, Aix-Marseille University,
Marseille, France
Victor I. Shrira, School of Computing and Maths, Keele University, Keele,
Staffordshire, UK
C. Steve Suh , Department of Mechanical Engineering, Texas A&M University,
College Station, TX, USA
Jian-Qiao Sun, School of Engineering, University of California, Merced, Merced,
CA, USA
J. A. Tenreiro Machado , ISEP-Institute of Engineering, Polytechnic of Porto,
Porto, Portugal
Simon Villain-Guillot , Laboratoire Ondes et Matière d’Aquitaine, Université de
Bordeaux, Talence, France
Michael Zaks , Institute of Physics, Humboldt University of Berlin, Berlin,
Germany
NonlinearPhysicalSciencefocusesonrecentadvancesoffundamentaltheoriesand
principles,analyticalandsymbolicapproaches,aswellascomputationaltechniques
in nonlinear physical science and nonlinear mathematics with engineering
applications.
Topics of interest in Nonlinear Physical Science include but are not limited to:
(cid:129) New findings and discoveries in nonlinear physics and mathematics
(cid:129) Nonlinearity, complexity and mathematical structures in nonlinear physics
(cid:129) Nonlinear phenomena and observations in nature and engineering
(cid:129) Computational methods and theories in complex systems
(cid:129) Lie group analysis, new theories and principles in mathematical modeling
(cid:129) Stability, bifurcation, chaos and fractals in physical science and engineering
(cid:129) Discontinuity, synchronization and natural complexity in physical sciences
(cid:129) Nonlinear chemical and biological physics
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Tosubmitaproposalorrequestfurtherinformation,pleasecontactDr.Mengchu
Huang(Email: [email protected]).
More information about this series at http://www.springer.com/series/8389
Dimitri Volchenkov
Editor
Nonlinear Dynamics, Chaos,
and Complexity
In Memory of Professor Valentin Afraimovich
123
Editor
Dimitri Volchenkov
Department ofMathematics andStatistics
Texas TechUniversity
Lubbock,TX, USA
ISSN 1867-8440 ISSN 1867-8459 (electronic)
Nonlinear Physical Science
ISBN978-981-15-9033-7 ISBN978-981-15-9034-4 (eBook)
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Preface
The present volume on Nonlinear Dynamics, Chaos, and Complexity explores
recent developments in experimental research representing a new step into our
understanding of complex dynamical systems and the relation between their
structure and functions. The volume is dedicated to the memory of our colleague
Valentin Afraimovich (1945–2018), a visionary scientist, respected colleague,
generous mentor, and loyal friend. Professor Afraimovich was a Soviet, Russian,
and Mexican mathematician known for his works in dynamical systems theory,
qualitative theory of ordinary differential equations, bifurcation theory, concept of
attractor, strange attractors, space-time chaos, mathematical models of nonequi-
librium media and biological systems, traveling waves in lattices, complexity of
orbits, and dimension-like characteristics in dynamical systems.
The volume opens with a memoir of Ms. Alexandra Afraimovich, the daughter
of Prof. Afraimovich. The rest of the volume represents an important collection of
workspresentsrecentadvancesindiscontinuousandnonlineardynamicalsystems,
chaos, and complexity science, important to understand resonance interactions in
nonlinear and discontinuous dynamical systems. The authors discuss analytical
solutions, the effect of time-delays, decisions under uncertainty, human-inspired
network dynamics, and urban spatial networks. Nonlinear Dynamics and
Complexityinvites readers toappreciate thisincreasinglymain-stream approachto
understandingcomplexphenomenainnonlinearsystemsastheyareexaminedina
broad array of disciplines. The book facilitates a better understanding of the
mechanismsandphenomenainnonlineardynamicsanddevelopsthecorresponding
mathematical theory to apply nonlinear design to practical engineering.
ValentinAfraimovichwasagenerous,gregarious,energeticpresenceatthevery
heartofnonlineardynamicsandcomplexitysciencecommunities,allofwhichwere
transformed by his presence. We hope that the scientific community will benefit
from this edited volume.
Lubbock, TX, USA Dimitri Volchenkov
v
Contents
Professor Valentin Afraimovich . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Alexandra Afraimovich
The Need for More Integration Between Machine Learning
and Neuroscience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Adrián Hernández and José M. Amigó
Quasiperiodic Route to Transient Chaos in Vibroimpact System. . . . . . 21
Victor Bazhenov, Olga Pogorelova, and Tatiana Postnikova
ModelingEnsemblesofNonlinearDynamicSystemsinUltrawideband
Active Wireless Direct Chaotic Networks. . . . . . . . . . . . . . . . . . . . . . . . 47
A. S. Dmitriev, R. Yu. Yemelyanov, M. Yu. Gerasimov,
and Yu. V. Andreyev
Verification of Biomedical Processes with Anomalous Diffusion,
Transport and Interaction of Species . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Messoud Efendiev and Vitali Vougalter
Chaos-Based Communication Using Isochronal Synchronization:
Considerations About the Synchronization Manifold . . . . . . . . . . . . . . . 75
J. M. V. Grzybowski, E. E. N. Macau, and T. Yoneyama
A Sequential Order of Periodic Motions in a 1-Dimensional,
Time-Delay, Dynamical System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Siyuan Xing and Albert C. J. Luo
On the Geometric Approach to Transformations of the Coordinates
of Inertial Frames of Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
A. A. Talyshev
Corpuscular Models of Information Transfer in a Random
Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
V. V. Uchaikin
vii
viii Contents
Kinetic Equation for Systems with Resonant Captures
and Scatterings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
A. V. Artemyev, A. I. Neishtadt, and A. A. Vasiliev
Solvability in the Sense of Sequences for Some Non-Fredholm
Operators in Higher Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Vitali Vougalter and Vitaly Volpert
Professor Valentin Afraimovich
AlexandraAfraimovich
ValentinAfraimovich(April2,1945–February21,2018).Aworld-renownedscholar,
doctor of physical and mathematical sciences. Valentine’s work has brought him
internationalrecognitioninthelate70s,whenhewasstillayoungscientistfromthe
city of Gorky, nowadays Nizhny Novgorod, Russia. Since 1991, Mr. Afraimovich
livedandworkedabroad,occasionallypayingvisitstohishomelandinRussia.
ValentineAfraimovichwasborninthesmalltownofBogorodsk,nearthecityof
NizhnyNovgorod.HisfatherAlexanderAfraimovichwasawell-respectedagricul-
turist.In1941,whilestillincollege,AlexanderenlistedasavolunteertofightNazis
in WWII. In the course of terrible fights near Smolensk he was wounded in both
legsandsentbackhometofinishhisstudies.Valentine’smother,AnnaKubyshkina,
descended from a large upper-class merchant family that lived in Bogorodsk for
many generations. She was drafted in the fall of 1941, right after she graduated
B
A.Afraimovich( )
Ensenada,Mexico
e-mail:[email protected]
©HigherEducationPress2021 1
D.Volchenkov(ed.),NonlinearDynamics,Chaos,andComplexity,
NonlinearPhysicalScience,https://doi.org/10.1007/978-981-15-9034-4_1
2 A.Afraimovich
fromheracceleratedsenioryearattheMoscowMedicalInstitute.Annaworkedas
amilitarysurgeononthefrontline,receivedseveralmedalsforbraveryandin1944
wasallowedtoreturntoherhometownofBogorodskwhereshebeganworkingasa
doctorinalocalhospital.
Aftergraduatingfromhighschoolin1963,ValentineAfraimovichappliedtothe
top school in the USSR—Moscow State University. He aced the entrance exams,
but alas, the state-sanctioned anti-semitism was rampant in the Soviet Union, and
Valentine, just like the majority of the applicants with Jewish last names, has not
beenaccepted.Theofficialexcuseforhisrejectionwasasubstandardperformancein
physics—examinerstoldthefutureworld-renownedmathematicianthathisapproach
tophysicsistoomath-oriented.
Fortunately, during that time Gorky State University had a wonderful practice
of waiving entrance exams for the best applicants who were rejected by the top
MoscowandKievuniversities.Thus,inadvertently,Gorkybecameahavenforthe
talentedyouthfromallovertheSovietUnion.Thisgavethehistoricallymerchant
city,nicknamed“thepurseofRussia”,areputationofbeingarelativelyliberaland
sophisticatedprovincialhub.