Director:
Professor Tassos Bountis
Department
of Mathematics,
E-mail:
bountis@math.upatras.gr
http://www.math.upatras.gr/~crans
C.R.A.N.S:
Tel. +30 2610 996742
The
Center for Research and Applications of Nonlinear Systems (C.R.A.N.S) was
founded by the Senate of the University
of
The
main purpose of C.R.A.N.S is to contribute to the advancement of research and
educational activities of scientists of the University
of
More
specifically, C.R.A.N.S aims to:
Promote
interdisciplinary research collaborations on nonlinear and complex systems
of applied sciences.
Organize
lectures and seminars on the most recent developments in Nonlinear Dynamics
and the Science of Complexity.
Develop
new educational methods for teaching the ideas and methods of Nonlinear
Dynamics at the undergraduate and graduate level.
Help
in the organization of International and Pan Hellenic Conferences and Summer
Schools on nonlinear systems.
The
members of C.R.A.N.S are faculty members and graduate students of the
From
the
Mathematics
(T. Bountis, Professor)
Physics
(D. Ghikas, Associate Professor)
Biology
(G. Yannopoulos, Professor)
Chemistry
(G. Maroulis, Professor)
Geology
(N. Lambrakis, Associate Professor)
From
the
Electrical
Engineering (Professors
Chemical
Engineering (Professors J.
Tsamopoulos, C. Cravaris)
Mechanical
Engineering (Associate Professors
Computer
Engineering and Informatics (Professor Th. Papatheodorou)
Engineering Science (Associate professor K. Papadakis)
From
the Health Sciences:
Department
of Medicine (Professors A. Bezerianos, G. Kostopoulos)
The
main research interests of C.R.A.N.S members include:
Nonlinear
Ordinary and Partial Differential Equations
Nonlinear
Difference Equations and Discrete Dynamics (Mappings,
Cellular Automata, Time Series, Neural Networks, Genetic Algorithms)
Dynamical
Systems, Chaos, Nonlinear Waves, Solitons and Fluid Dynamics
Nonlinear
Oscillations in Lattices, Electrical Circuits, Population Dynamics
Applications
of Nonlinear Dynamics to Cardiac and Brain Electrical
Activity, Nonlinear Time Series in Meteorology, Geology and
Economics.
Other
activities of C.R.A.N.S. include:
Publication
of scientific papers co-authored by C.R.A.N.S members
emphasizing collaboration with other Departments and Institutes
Submission
of proposals to research and educational programmes of
1999-2001:
P.I. of a PENED grant on ''Applications of Nonlinear Dynamics to Biological
and Biochemical Systems''. Greek Ministry of Development, General
Secretariat of Research and Technology (GSRT).
2000-01:
Supervisor of Marie Curie Fellowship by Dr. Elka Yankulova on ''Dimensional
and Genetic Analysis of Drosophila Cardiac Function'', EEC, European
Research programme on "Quality of Life and Management of Living
Resources".
2000-02:
P.I. of a Research Exchange Programme between
2001-03:
P.I. of a Research "Caratheodory" Programme of the
2002-05:
P.I. of a Research grant of the "HERAKLEITOS" Programme of the
Greek Ministry of Education, supporting the doctoral candidate Mr. Christos
Antonopoulos.
2005-07:
P.I. of a Research grant of the "PYTHAGORAS II" Programme of the
Greek Ministry of Education, supporting the post – doctoral candidate Mr.
Vassilios Basios.
2004
-2005: Representative of
2006
-2008: Representative of
2004
Series:
January
29 and February 5:
Professor Kostas Cravaris, Dept. of Chemical Engineering,
University
of
Title: The
Luenberger Observer for Linear Dynamical Systems and its Generalization to
Nonlinear Dynamical Systems
March
26: Professor
Serguei Foss,
Title: Backwards
coupling: stability and perfect simulation.
April
2, 23, 30,
May 7: Dr. Susumu
Tanabe,
Lecture
series: Algebraically Integrable Systems and Hyperelliptic Functions
Lecture
5: The Theta-Functions
Lecture
6: Integrability of the Rotating Rigid
Body
Lecture
7: Integrability of the Kowalevskaya Case
Lecture
8: The Kowalevskaya –Painleve Criterion
May
5:
Dr. Jacob P. van der Weele,
Title:
Differential Equations with Applications to Physics, Technology and
Traffic Flow
November
4: Zsolt Sandor,
Postdoctoral Researcher of Astronomy,
Title:
The
Relative Lyapunov Indicator and its application to planetary systems.
November
11: Moses Boudourides,
Associate Professor, Dept. Of
Mathematics, University
of
Title:
Properties
of Networks of Small Worlds of Networks with Power Law Distributions
December
16: Pavlos Soulis, Graduate
student of the Department of Mathematics,
Title:
A
Review of Analytical Studies of the Sitnikov 3 Body Problem
2005
Series:
January
21:
Dr. Christos Efthymiopoulos,
Title:
The Nekhoroshev Theory of Stability in Nonlinear Hamiltonian Systems
February
11:
Dr. Christos Efthymiopoulos, Research
Title:
Birkhoff Normal
Form in Hamiltonian Systems of n>1 Degrees of
October
20: Ch. Antonopoulos,
Graduate student of the Department of Mathematics,
Title:
Stability of Hamiltonian Systems of n Degrees of Freedom: From
October
27: A.
Manos, Graduate student of the Department of Mathematics,
Title:
Chaotic and Regular Solutions of Nonlinear Models of Galactic Dynamics
November
3: D. Nomikos,
Graduate student of the Department of Mathematics,
Title:
Nonintegrability
of Hamiltonian Systems
November
7:
P. G. L. Leach, Professor, Mathematics Department, University of
Title:
Models of Financial Mathematics: Linear and Nonlinear
November
24:
Title:
Mathematical
Simulation of Structural and Dynamical Properties of
2006 Series:
February
16:
Tassos Bountis, Professor, Department of Mathematics, University
of
Title:
A
New Geometrical Method for Studying Chaos and Order in
March
2: Ch. Antonopoulos
and Y. Petalas,
Graduate students of the
Title:
Chaos
and Order in Multidimensional Hamiltonian Systems:
A Combination
of Nonlinear Dynamics and Evolutionary Algorithms
March
16: Dr. Laura Cimponeriu, Post-doctoral
Fellow, Department of Medicine,
Title:
Mathematical Models of Synchronization and Application to Electrical
April
6: I.
Bakas, Professor
of Physics Department, University of Patras
Title:
Geometric Evolution Equations and Some of Their Applications
April
10:
Title:
Introduction
to Dynamical Distributed Parameter Systems.
April
10: V. Basios, Post
– doctoral Fellow,
Title:
Symbolic
Dynamics and Low – Dimensional Chaos
April
11:
Title:
The
Optimal Measurement Problem
April
11: V. Basios, Post
– doctoral Fellow,
Title:
Probabilistic
Approach to Chaos and Statistical Aspects of Deterministic Dynamics.
April
12: Milan
Stehlik, Assistant
Professor, Department of Mathematics,
Title: Parameter
Estimation Methods and the Likelihood Ratio
April
12: V. Basios, Post
– doctoral Fellow,
Title:
The Principle of
Linear Stability Analysis in Nonlinear Systems
April
13:
Milan
Stehlik, Assistant
Professor, Department of Mathematics,
Title:
Correlation and Maximal Likelihood Estimation
April
13: V. Basios, Post
– doctoral Fellow,
Title:
Reaction Diffusion Systems, Pattern Formation and Morphogenesis
May
4: Jacob P. van der Weele, Associate
Professor of Mathematics,
Title: Granular
Matter: A New Form of Solid, Liquid and Gas!
May
11: Dr. Αhmet
Yantir, Deparetment
of Mathematics,
Title:
Self – Adjoint Dynamical Equations in Different Time Scales
July
6:
Angela de Sanctis, Associate
Professor, Department of Quantitative Methods
and Economic Theory, University”G. d’Annunzio” of
Chieti-Pescara,
Italia
Title:
Modelling Commodity Prices by Stochastic Differential Equations.
Participation
in the organization of the 9th Summer School/Pan Hellenic
Conferences on “Nonlinear Dynamics,
Chaos and Complexity” at Patras (1996), 10th
at Thessalonica (1997), 11th at Livadeia (1998), 12th at
Patras (1999) and 13th at Chania,
The
organization of the 14th Summer School/Pan Hellenic Conference,
at Patras, July 23 –
16th
Summer School/Pan-Hellenic Conference) on ''Nonlinear Systems and Chaotic
Dynamics", at Chalkida, July 2003.
Co
– Organizer with Professor
Main
Organizer the International Summer School and Conference on ''Complexity in
Science and Society'', 14 – 26 July, 2004, Patras and
Co
– Organizer of the 18th Summer School/Pan-Hellenic Conference on
''Nonlinear Science and Complexity",
Co
– Organizer with Prof. E. Aifantis of the
National
National
Academy
of
University
of Thessaly, Polytechnic School, Department of Mechanical Engineering
(Professor Nicholas Vlachos and Th. Karakasidis) and Department of
Pedagogics (Professor D. Vavougios)
The
The
Center for Nonlinear Studies of the University of
MIDIT,
Center for Mathematical Modelling and Nonlinear Dynamics,
Center
for Applied Mathematics and Theoretical Physics,
Institute
for Theoretical Physics,
Instituto
Pluridisciplinar, University Complutense of
Department
of Applied Mathematics and Theoretical Physics,
Max
Planck Institute for Complex Systems,
Department
of Mathematics,
Universite
de Provence (Marseille I) Observatoire de l’Astronomie (Dr. Lia
Athanassoula)
S.
Papadimitriou
, A. Bezerianos and T. Bountis, “Real-Time Encryption
with Chaotic Systems of Difference Equations”, IEE Trans. On Comp. 46 (1) (1997) 27.
M.
N. Vrahatis, H.Isliker and T. Bountis, “Structure and Breakdown of
Invariant Tori in a 4-D Mapping Model of Accelerator Dynamics”, Int. J.
Bifurc. Chaos 7(12) (1997) 2707 .
T.
Bountis, H. Isliker, M. Kollmann and M.N. Vrahatis, “Stability and
Diffusion in 4-D Mapping Models
of Accelerator Dynamics”, Proc. of Conf. on Nonlinear and Stochastic Beam
Dynamics, ed. H.
Mais, DESY Report 97-161 (1998).
S.
Papadimitriou, A. Bezerianos and T. Bountis, “Radial Basis Function
Networks as Chaotic Generators for Secure Communication Systems”, Int. J.
of Bifurc. Chaos 9(1) (1999) 221.
T.
Bountis, C. F. Starmer and A. Bezerianos, “Solitary Pulses and Wave Front
Formation in an Excitable Medium”, Prog. Theor. Phys. Suppl. 139
(2000)12-33.
N.
Lambrakis, A. Andreou, P. Polydoropoulos, E. Georgopoulos, T. Bountis, “
Nonlinear Analysis and Forecasting of a Salt Water Karstic Spring”, Water
Resources Research, 36(4)(2000)
875-884.
A.
Andreou, A. Karytinos and G. Pavlides, “ Nonlinear Time Series Analysis of
the Greek Exchange Rate Market”, Intern. J. Bifurc. Chaos,
10 (7) (2000) 1729-1758.
S.
Papadimitriou, T. Bountis,
S.
Papadimitriou
, A. Bezerianos, T. Bountis and G. Pavlides, ''Secure
Communication Protocols With Discrete Nonlinear Chaotic Maps'', J. Syst.
Archit. 47 61-72 (2001).
J.
S. Nicolis, T. Bountis and K. Togias, "The Dynamics of Self-Referential
Paradoxical Games", Dynamical Systems, 16 (4), 319 - 332 (2001).
T.
Karakasidis and
P.
A. Patsis, Ch.
Skokos
& E. Athanassoula, "Orbital dynamics of three-dimensional bars:
III. Boxy/Peanut edge-on profiles", MNRAS, 337, 578-596 (2002).
Ch.
Skokos
& A. Dokoumetzidis, "Study of the effective stability in the
spatial restricted problem of three bodies", in Order and Chaos in
Non-linear Dynamical Systems, Vol. 7 eds. Bountis T. C., Ellinas D.
& Grispolakis I., Pnevmatikos G. A., Athens, (2002) 113-118.
C.
Polymilis, G. Servizi, Ch. Skokos,
G. Turchetti & M. N. Vrahatis, "Topological degree theory and local
analysis of area preserving maps", Chaos, 13, 1, (2003)
94-104.
Ch.
Skokos, Ch. Antonopoulos, T. C. Bountis & M. N. Vrahatis, "How
does the Smaller Alignment Index (SALI) distinguish order from chaos?",
Prog. Theor. Phys. Supp., 150 (2003) 439.
C.
Polymilis, G. Servizi, Ch. Skokos,
G. Turchetti & M. N. Vrahatis, "Locating periodic orbits by
Topological Degree theory", in Proceedings of International Conference
on Libration Point Orbits and Applications (2003) (in press).
A.
Leontitsis, J. Prange and T. Bountis, "Large Noise Level
Estimation", Int. J. Bifurc. Chaos
13 (8) (2003) 2309.
J.E.
Skinner, E.D. Yankulova, G. Yannopoulos and T. Bountis, "Nonlinear
Analysis of a Drosophila ECG Time Series", Dros. Inf. Serv.
85 (2003)
111.
Laura
Cimponeriu, Michael Rosenblum, and Arkady Pikovsky, "Estimation of
delay in coupling from time series", (2004) (in press).
Ch.
Skokos, C. Antonopoulos, T. Bountis and M. N. Vrahatis, “Detecting Order
and Chaos in Hamiltonian Systems by the SALI Method", J. Phys. A: Math.
Gen., 37, 6269-6284 (2004).
P.
Panagopoulos, T. Bountis and C. Skokos, "Existence and Stability of
Localized Oscillations in 1-D Lattices With Soft Spring and Hard Spring
Potentials", ASME Transactions, Journal of Vibration and Acoustics,
vol. 126, 520 – 527 (October 2004).
G.
M. Mahmoud and T. Bountis, "The Dynamics of Complex Nonlinear
Oscillators: A Review", Intern. J. of Bifurcation and Chaos, vol. 14
(11) Vol. 14, 3821-3846, (2004) .
C.
Efthymiopoulos, T. Bountis and A. Manos, “Explicit Construction of
Integrals with Quasi-Monomial Terms from the Painleve Series”, Regular and
Chaotic Dynamics, vol. 9, no. 3, p. 385 – 398 (2004).
C.
Antonopoulos, T. Bountis and Ch. Skokos, “Chaotic Dynamics of N – Degree
of Freedom Hamiltonian Systems”, Int. Journal Bifurc. Chaos, to appear,
June 2006.
P.
Soulis, T. Bountis and R. Dvorak, “Stability of Motion in the Sitnikov 3
– Body Problem”, preprint submitted for publication, 2006.
P.
Maniadis and T. Bountis, ‘Quasiperiodic and Chaotic Breathers in a
Parametrically Driven System Without Linear Dispersion”, to appear in PRE,
2006.
Director:
Professor
Tassos Bountis
Professor
Sp. Pnevmatikos
Professor
D. Tsoubelis
Professor
N. Kafoussias
Associate
Professor V. Papageorgiou
Associate
Professor J. P. van der Weele
Dr.
V. Basios, 2005 – 2007, PhD, Free
Dr.
Charalambos Skokos, 2003 – 2005,
Dr.
Christos Efthymiopoulos, Visiting Scientist,
Dr.
Susumu Tanabe, 2002 – 2004,
Complexity
and Complex Dynamical Systems
Nonlinear
Dynamics and Chaos
Ordinary
and Partial Nonlinear Differential Equations
Nonlinear
Waves and Solitons
Nonlinear
Difference Equations
Periodic
solutions, stability analysis and bifurcation theory
Integrability
and the Painleve Property
Nonlinear
Time Series Analysis
Geometry
and Mechanics
Applications to Physics, Chemistry and Biology
Main Researcher:
Professor
Michael N. Vrahatis
The
Computational Intelligence Group (CIGroup) has been established at the Department of Mathematics at the
University of Patras, Greece. The
group aims at the advancement of pure and applied research, as well as,
education in the fields of computational intelligence and natural computing.
The
main objectives of the CIGroup evolve around four axes:
The
investigation and mathematical foundation of methods in computational
intelligence and natural computing.
The
development of innovative methods in these fields.
The
application of the acquired expertise to address challenging real-life
problems in different branches of science.
The
dissemination of knowledge to undergraduate and postgraduate students.
Cryptography:
Application
of Swarm Intelligence
methods in a number of challenging problems including:
Dynamical
systems:
This
research has been published in various journals including Neural Computation,
IEEE Transactions on Neural Networks, Artificial Intelligence, Neural Networks,
Neural Processing Letters, Nonlinear Analysis, Natural Computing, Journal of
Complexity, Journal
of Computational and Applied Mathematics, Applied Numerical
Mathematics, Neural, Parallel and Scientific Computations, Chaos,
Nonlinearity, Journal of Computational Physics, International Journal of
Bifurcation and Chaos,
Main
researcher: Anastasios
Bezerianos, Professor
Laura Cimponeriu,
Post – Doctoral Researcher
Andrei Dragomir,
Post – Doctoral Researcher
Liviu Moraru,
Post – Doctoral Researcher
Ioannis
Maraziotis, Doctoral student
Hugues
Fontenelle, Doctoral student
Νicholas Tsarouhas, Doctoral student
Maria Stavrinou,
Doctoral
student
Charalambos
Nikas, Doctoral student
Diagnostic
Analysis of Heart Rate Time Series
Development
and numerical solution of mathematical models describing electrical
propagation in the myocardium, aiming to simulate effects of ischemia and
arrhythmia.
ECG
Analysis of Magnetoencephalograms (MEG)
using auditory evoked magnetic fields to study memory traces with different
lifetimes.
Application
of Computational Intelligence methods
to biological signal analysis
Analysis
of Genomic sequences from large data bases (Bioinformatics)
Department
of Physics, University of Potsdam, Potsdam, Germany
(prof. M. Rosenblum)
Department
Biomedical Engineering, School of Medicine, The Johns Hopkins University,
Baltimore MD, USA (Prof. Nitish
Thakor)
Humαn
Brain Dynamics Lab, Brain Sciences Institute (RIKEN), Saitama, Japan (Dr
Andreas Ioannides)
Department
of Biometry/Epidemiology, Medical University of S. Carolina, Charleston SC,
USA (Prof. Frank Starmer)
Department
of Neurology, Clinical Neurophysiology Lab, SUNY, New York, NY, USA
(Prof. Ivan Bodis Wollner)
Department
of Electrotechnics, Technical University
of Bucharest, Bucharest, Romania (Prof. Paul Cristea).
Johns Hopkins
University,
USA,
prof. N. Thakor
Jiao Tong University, CHINA, prof.
Y. Zhu and S. Tong
Technical University of Bucharest,
ROMANIA, prof. P. Cristea
University of Chieti. ITALY,
prof. V. Pizzella
University of Potsdam, GERMANY,
prof. J. Kurth and M. Rosenblum
International University of Florida,
USA, prof. N. Tsoukias