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|Title: ||Bifurcation analysis of piecewise-linear systems with hysteresis nonlinearity|
|Other Titles: ||Ju you chi zhi fei xian xing de fen duan xian xing xi tong de fen zhi fen xi|
|Authors: ||He, Yangbo (何楊波)|
|Department: ||Department of Mathematics|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2008|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Linear control systems.|
|Notes: ||CityU Call Number: TJ220 .H43 2008|
vi, 119 leaves : ill. 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2008.
Includes bibliographical references (leaves -119)
|Abstract: ||A perturbation-incremental (PI) method is presented for the computation, continuation,
bifurcation analysis of periodic solutions and homoclinic and heteroclinic orbits of
piecewise-linear systems and systems with hysteresis nonlinearity. We first study the
computation of homoclinic and heteroclinic orbits of piecewise-linear system. From
the continuation in a bifurcation parameter using the PI method, high codimension
points can be obtained, which give useful information of how the dynamics of the
system is organized. The Chua’s circuit is used as an illustration.
Next, we study a two-degree-of-freedom aeroelastic system with hysteresis nonlinearity.
Explicit form of a limit cycle with arbitrary parameter values can be obtained,
which enables the phase portraits to be constructed. Periodic solutions can be calculated
and their stabilities are determined by means of the Poincar´e map. As the parameter
varies, bifurcations such as period-doubling, symmetric-breaking, saddle-node and
Hopf-like bifurcations can be identified. In particular, we find two narrow intervals in
which period-doubling sequence to chaos is observed. From the above investigation,
the advantage of the PI method lies in its simplicity and ease of implementation.
It is well known that chaos does not occur in a two-dimensional continuous autonomous system. For a two-dimensional piecewise-linear system with hysteresis nonlinearity,
the flow at a point in the phase plane may not be unique. Therefore, a trajectory
may traverse itself. We investigate the properties of such a system and obtain a
chaos attractor using an one-dimensional map.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2340683|
|Appears in Collections:||MA - Doctor of Philosophy |
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