Cauchy problem. Systems of differerential equations The phase. Qualitative theory.The logistic model. Competition. Predator-prey model. Models in epidemiology: SIS, SIR . The Van Der Pol equation. Duffing equation. Lienard equation. Massera’s Theorem.
W. Boyce-R. Di Prima Elementary differential equations and boundary value problems. Wiley
M. Iannelli Appunti di dinamica di popolazioni. Università di Trento
Learning Objectives
Knowledge acquired:
Basic concepts of the theory of differential equations.
Competence acquired:
Knolewdge of the standard models in dynamic of populations and epidemiology. Knolewdge of the main results in the qualitative theory of planar dynamical systems.
Skills acquired (at the end of the course):
Capability of analyzing a mathematical model. Skills necessary for the study of dynamical planar systems.
Prerequisites
Courses required: Mathematical Analysis II.
Teaching Methods
CFU: 6
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 150
Hours reserved to private study and other individual formative activities: 108
Frequency of lectures, practice and lab: Recommended
Teaching Tools UniFi E-Learning: http://e-l.unifi.it
Office hours:
Thursdays, 15:00-17:00, or by appointment.
Dipartimento di Matematica "Ulisse Dini"
Viale Morgagni, 67/a
50134 - Firenze (FI)
Tel: 055 4237117 Fax: 055 4237165
gabriele.villari@unifi.it, gabriele.villari@math.unifi.it
Type of Assessment
Oral
Course program
Cauchy problem. Non uniqueness of solutions. Peano example. Persistence of solutions. Maximal solutions Gronwall’s lemma. Systems of differerential equations The phase plane. Singular points. Quasi linear systems. Qualitative theory. Dynamic of populations. The logistic model. Competition. The principle of exclusion. Predator-prey model Volterra’s theorem. Models in epidemiology: SIS, SIR and mixed. The Van Der Pol equation and his phase-portrait. Existence and uniqueness of limit cycles. Liénard equation and his ph