scholarly journals Energy-optimal steering of transitions through a fractal basin boundary

2004 ◽  
Author(s):  
A.N. Silchenko ◽  
S. Beri ◽  
D.G. Luchinsky ◽  
V.E. McClintock
Keyword(s):  
Basin Boundary ◽  
Fractal Basin Boundary

scholarly journals Fluctuational Transitions through a Fractal Basin Boundary

2003 ◽  
Vol 91 (17) ◽  
Author(s):  
A. N. Silchenko ◽  
S. Beri ◽  
D. G. Luchinsky ◽  
P. V. E. McClintock
Keyword(s):  
Basin Boundary ◽  
Fractal Basin Boundary

Noise and Chaos in a Fractal Basin Boundary Regime of a Josephson Junction

1985 ◽  
Vol 55 (7) ◽  
pp. 746-749 ◽  
Author(s):  
M. Iansiti ◽  
Qing Hu ◽  
R. M. Westervelt ◽  
M. Tinkham
Keyword(s):  
Josephson Junction ◽  
Basin Boundary ◽  
Fractal Basin Boundary

Fractal basin boundary in dynamical systems and the Weierstrass-Takagi functions

1988 ◽  
Vol 128 (9) ◽  
pp. 470-478 ◽  
Author(s):  
Yoshihiro Yamaguchi ◽  
Kiyotaka Tanikawa ◽  
Nobuhiko Mishima
Keyword(s):  
Dynamical Systems ◽  
Basin Boundary ◽  
Fractal Basin Boundary

Fractal basin boundary of a two-dimensional cubic map

1985 ◽  
Vol 109 (5) ◽  
pp. 196-200 ◽  
Author(s):  
Y. Yamaguchi ◽  
N. Mishima
Keyword(s):  
Two Dimensional ◽  
Basin Boundary ◽  
Fractal Basin Boundary

ALFVÉN COMPLEXITY

2008 ◽  
Vol 18 (06) ◽  
pp. 1697-1703 ◽  
Author(s):  
E. L. REMPEL ◽  
A. C.-L. CHIAN ◽  
D. KOGA ◽  
R. A. MIRANDA ◽  
W. M. SANTANA
Keyword(s):  
Complex System ◽  
Gaussian Noise ◽  
Complex Dynamics ◽  
Alfven Wave ◽  
Basin Boundary ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Fractal Basin Boundary ◽  
Non Gaussian ◽  
Qualitative Changes ◽  
Chaotic Saddle

The complex dynamics of Alfvén waves described by the derivative nonlinear Schrödinger equation is investigated. In a region of the parameters space where multistability is observed, this complex system is driven towards an intermittent regime by the addition of noise. The effects of Gaussian and non-Gaussian noise are compared. In the intermittent regime, the Alfvén wave exhibits random qualitative changes in its dynamics as the result of a competition between three attractors and a chaotic saddle embedded in the fractal basin boundary.

CHARACTERIZING FRACTAL BASIN BOUNDARIES FOR PLANAR SWITCHED SYSTEMS

Fractals ◽  
2017 ◽  
Vol 25 (03) ◽  
pp. 1750031 ◽  
Author(s):  
YONGXIANG ZHANG
Keyword(s):  
Switched Systems ◽  
Auxiliary System ◽  
Fractal Basin Boundaries ◽  
Basin Boundary ◽  
Prime Ends ◽  
Fractal Basin Boundary ◽  
Type 3 ◽  
Analytical Tools ◽  
Prime End ◽  
Basin Boundaries

This paper is to introduce some analytical tools to characterize the properties of fractal basin boundaries for planar switched systems (with time-dependent switching). The characterizing methods are based on the view point of limit sets and prime ends. By constructing the auxiliary dynamical system, the fractal basin boundaries of planar switched systems can be proved if every diverging path in the basin of associated auxiliary system has the entire basin boundary as its limit set. Fractal property is also verified if every prime end that is defined in the basin of associated auxiliary system is a prime end of type 3 and all other prime ends are of type 1. Bifurcations of fractal basin boundary are investigated by analyzing what types of prime ends in the basin are involved. The fractal basin boundary of switched system is also described by the indecomposable continuum.

Fractal basin boundary constructed by superposition of the Weierstrass function

1986 ◽  
Vol 117 (9) ◽  
pp. 450-458 ◽  
Author(s):  
Yoshihiro Yamaguchi ◽  
Kiyotaka Tanikawa
Keyword(s):  
Weierstrass Function ◽  
Basin Boundary ◽  
Fractal Basin Boundary

Indeterminate jumps to resonance from a tangled saddle-node bifurcation

1991 ◽  
Vol 432 (1884) ◽  
pp. 101-111 ◽  
Keyword(s):  
Unstable Manifold ◽  
Saddle Node Bifurcation ◽  
Dissipative Dynamics ◽  
Basin Boundary ◽  
Saddle Node ◽  
Evolving System ◽  
New Type ◽  
Fractal Basin Boundary

We identify in this paper a new type of bifurcation which yields an unpredictable outcome and therefore seems to be an important new ingredient of nonlinear dissipative dynamics. It arises when the unstable manifold of the saddle of a saddle-node bifurcation is heteroclinically tangled with the inset of a distant saddle which is itself homoclinically tangled so that it forms a fractal basin boundary between two remote attractors. At the saddle-node fold, a slowly evolving system will thus find itself sitting precisely on a fractal basin boundary, and in the presence of even infinitesimal noise we cannot predict to which of the two remote attractors the system will jump. We show here that such an indeterminate tangled saddle-node bifurcation is a common ingredient in the resonance of softening systems.

On the Fractal Structure of Basin Boundaries in Two-Dimensional Noninvertible Maps

2003 ◽  
Vol 13 (07) ◽  
pp. 1767-1785 ◽  
Author(s):  
A. Agliari ◽  
L. Gardini ◽  
C. Mira
Keyword(s):  
Fractal Structure ◽  
Real Plane ◽  
Two Dimensional ◽  
Numerical Examples ◽  
The Real ◽  
Basin Boundary ◽  
Fractal Basin Boundary ◽  
Noninvertible Maps ◽  
Analytical Tools ◽  
Basin Boundaries

In this paper we give an example of transition to fractal basin boundary in a two-dimensional map coming from the applicative context, in which the hard-fractal structure can be rigorously proved. That is, not only via numerical examples, although theoretically guided, as often occurs in maps coming from the applications, but also via analytical tools. The proposed example connects the two-dimensional maps of the real plane to the well-known complex map.

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