Authors:
MingQing Xiao,
Volume: 1, Page 2050 Paper number 1801
Abstract:
A class of diffusively coupled oscillators is discussed. The model
is governed by reaction-diffusion equations with nonlinear boundary
conditions. The two linear uncoupled equations describe the diffusion
process, while the nonlinear boundary conditions describe all reaction
and interaction. By using the boundaru conditions, the system can
be translated into two uncoupled oscillators of two dimensions, it
is found that the Hopf bifurcations are always degenerate due to the
internal resonance of the coupled system.
Authors:
Xinghuo Yu,
Guanrong Chen,
Yanxing Song,
Zhenwei Cao,
Yang Xia,
Volume: 1, Page 2054 Paper number 1802
Abstract:
In this paper, we discuss a generalization of the OGY chaos control
method based on the invariant manifold theory. This control methodology
can deal with higher order chaotic systems in the same spirit of the
OGY method. The effectiveness of the methodology will be tested by
controlling the third order Rossler chaos.
Authors:
Goong Chen,
Tingweng Huang,
Sze-Bi Hsu,
Volume: 1, Page 2060 Paper number 1803
Abstract:
In this paper, we analyze the dynamical behavior of the linear wave
equation on an interval, where the right endpoint has a van der Pol
type nonlinearity or boundary controller, while the left endpoint has
a boundary condition involving displacement. The asymptotic behavior
of the system can be classified into two basic types: classical unbounded
instability, or spatial pointwise convergence to periodic points of
a nonlinear map corresponding to the van der Pol condition.
Authors:
MingQing Xiao,
Wei Kang,
Volume: 1, Page 2066 Paper number 1804
Abstract:
We study the local feedback stabilization of Hopf bifurcations for
nonlinear systems of infinite-dimensions in the case where the linearized
vector field has a pair of simple nonzero imaginary eigenvalues and
all its other eigenvalues lie strictly in the left half-plane. Through
discussing the normal form of nonlinear systems obtained by the integral
averaging method, we discuss some conditions for controlling the stability
of the systems, provided that the critical modes are uncontrollable.
As an example, we apply the obtained results to the control of axial
flow compressor model.
Authors:
Diego Marcelo Alonso,
Eduardo Emilio Paolini,
Jorge Luis Moiola,
Volume: 1, Page 2072 Paper number 1806
Abstract:
In this paper, the control of the amplitude of the oscillations in
an underactuated mechanical system is treated. Two different procedures
for the design of the controller are proposed. One is based on Hopf
bifurcation theory, and the other is derived from considerations about
the system's energy. The performance of the designed controllers is
analyzed via numerical simulations. Experimental results for the energy-based
law are also included.
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