[Turkmath:1700] Gebze Teknik Üniversitesi Matematik Bölümü Seminerleri

[Işıl Öner]

Sayin Liste Uyeleri,

Gebze Teknik Üniversitesi (GTU) Matematik Bölümü Genel Seminerleri kapsamında,
9 Aralık Cuma günü saat 14:00'da Ayşegül Kıvılcım (İstanbul Aydın Üniversitesi) bir seminer  verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler davetlidir.

Saygılarımızla.

Dear all,

There will be a seminar in Gebze Technical University (GTU) on 9th of
December  by Ayşegül Kıvılcım (Istanbul Aydın University)
Time  and  place:  At 14:00 in Department of Mathematics, Building I, Seminar room.

Title: Discontinuous dynamics with grazing points

Abstract:

Discontinuous dynamical systems with grazing solutions are discussed.

The group property, continuation of solutions, continuity and smoothness

of motions are thoroughly analyzed. A variational system around a grazing

solution which depends on near solutions is constructed. Orbital

 stability of grazing cycles is examined by linearization. Small

 parameter method is extended for analysis of neighborhoods of

grazing orbits, and grazing bifurcation of cycles is observed

in an example. Linearization around an equilibrium grazing point

is discussed. The mathematical background of the study relies

 on the theory of discontinuous dynamical systems [1]. Our approach

 is analogous to that one of the continuous dynamics analysis and results

 can be extended on functional differential, partial differential equations

and others. Appropriate illustrations with grazing limit cycles and

bifurcations are depicted to support the theoretical results.

As an example, a coupled Van der Pol oscillators with impacts

is taken into account. In addition to these results, non-autonomous

grazing phenomenon is investigated through periodic systems and their

solutions. The analysis is different than for autonomous systems

in many aspects. Conditions for the existence of a linearization

have been found. Stability of a periodic solution and its persistence

 under regular perturbations are investigated. Through examples,

the theoretical results are visualized.

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