MODELS OF PHYSICAL MATHEMATICS
cod. 18975

Academic year 2016/17
3° year of course - Second semester
Professor
Academic discipline
Fisica matematica (MAT/07)
Field
Attività formative affini o integrative
Type of training activity
Related/supplementary
60 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in - - -

Learning objectives

Introduction to mathematical modelling through differential equations

Prerequisites

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Course unit content

Dynamical Systems. Equilibria and Stability. Lyapunov Methods.

Linear and nonlinear models in Mechanics.

Mathematical models in population dynamics.

Van der Pol equation.

Bifurcation theory, Hopf theorem, limit cycles.

Poincarè-Bendixon theorem.

Lorenz model and chaos.

Discrete dynamical systems. Feigenbaum map.

Full programme

Dynamical Systems. Equilibria and Stability. Lyapunov Methods.
Linear and nonlinear models in Mechanics.
Mathematical models in Population Dynamics.
Van der Pol equation.
Bifurcation theory, Hopf theorem, limit cycles.
Poincarè-Bendixon theorem.
Lorenz system and chaos.
Discrete dynamical systems. Feigenbaum map.

Bibliography

G.L. CARAFFINI, M. IORI, G. SPIGA, Proprietà elementari dei sistemi dinamici, Appunti per il corso di Meccanica Razionale, UNIVERSITA' DEGLI STUDI DI PARMA, a.a 1998-99;

G. BORGIOLI, Modelli Matematici di evoluzione ed equazioni differenziali, Quaderni di Matematica per le Scienze Applicate/2, CELID, TORINO, 1996;

R. RIGANTI, Biforcazioni e Caos nei modelli matematici delle Scienze applicate, LEVROTTO & BELLA TORINO, 2000;

M.W HIRSCH, S. SMALE, Differential Equations, Dynamical Systems and Linear Algebra, ACADEMIC PRESS, NEW YORK, 1974;

J.D. MURRAY, Mathematical Biology, SPRINGER-VERLAG, NEW YORK, 1989;

J. GUCKENHEIMER, P. HOLMES, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vectors Fields, SPRINGER-VERLAG, NEW YORK, 1983;

M. SQUASSINA, S. ZUCCHER, Introduzione all'analisi qualitativa delle equazioni differenziali ordinarie (ebook), APOGEO, 2008.

Teaching methods

Lectures and exercises

Assessment methods and criteria

Oral exam in addition to an autonomous project

Other information

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