zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Study of a class of hybrid-time systems. (English) Zbl 1133.34304
Summary: The aim of this paper is to study the dynamic behavior of a class of hybrid-time systems. In particular, we concern about switched systems constituted by two linear second order systems with a time varying (sinusoidal type) translation term. By means of numerical simulations, system behavior and its relation to system parameters are studied. It is shown that system eigenvalues play a crucial role in the time evolution of the system leading either to regular behavior, oscillatory patterns or intermittent erratic-periodic behavior. Furthermore, it is shown that under certain conditions, presumable fractal structures can be obtained.

34A36Discontinuous equations
34D05Asymptotic stability of ODE
34C28Complex behavior, chaotic systems (ODE)
Full Text: DOI
[1] Kaneko, K.: Recursiveness, switching and fluctuations in a replicating catalytic network. Phys rev E 68, 0319091-0319095 (2003)
[2] Glick, B. R. R.; Pasternak, J. J.: Molecular biotechnology: principles and applications of re-combinant DNA. (2002)
[3] Casado, J. M.; Baltanas, J. P.: Phase switching in a system of two noisy Hodgkin -- Huxley neurons coupled by a diffusive interaction. Phys rev E 68, 0619171-06191710 (2003)
[4] Banerjee, S.; Vergese, G. C.: Nonlinear phenomena in power electronics. Attractors, bifurcations, chaos and nonlinear control. (2001)
[5] Banerjee, S.; Chakrabarty, K.: Nonlinear modeling and bifurcations in the boost converter. IEEE trans power electron 13, 252-260 (1998)
[6] Banerjee, S.; Rahjan, P.; Grebogi, C.: Bifurcation in two-dimensional piecewise smooth maps: theory and applications in switching circuits. IEEE trans circ syst --- I 47, 633-643 (2000) · Zbl 1050.37511
[7] Zhusubaliyev, Z. T.; Soukhoterin, E. A.; Mosekilde, E.: Quasi-periodicity and border-collision bifurcations in a dc -- dc converter with pulsewidth modulation. IEEE trans circ syst --- I 50, 1047-1057 (2004)
[8] Ma, Y.; Kawakami, H.; Tse, C. T.: Bifurcation analysis of switched dynamical systems with periodically moving borders. IEEE trans circ syst --- I 51, 1184-1193 (2004)
[9] Caserta, F.; Eldred, D.: Determination of fractal dimension of physiologically characterized neurons in two and three dimensions. J neurosci methods 56, 133-144 (1995)