67,148 research outputs found
Unpredictable Points and Chaos
It is revealed that a special kind of Poisson stable point, which we call an
unpredictable point, gives rise to the existence of chaos in the quasi-minimal
set. The existing definitions of chaos are formulated in sets of motions. This
is the first time that description of chaos is initiated from a single motion.
The theoretical results are exemplified by means of the symbolic dynamics.Comment: 9 page
Existence of Unpredictable Solutions and Chaos
In paper [1] unpredictable points were introduced based on Poisson stability,
and this gives rise to the existence of chaos in the quasi-minimal set. This
time, an unpredictable function is determined as an unpredictable point in the
Bebutov dynamical system. The existence of an unpredictable solution and
consequently chaos of a quasi-linear system of ordinary differential equations
are verified. This is the first time that the description of chaos is initiated
from a single function, but not on a collection of them. The results can be
easily extended to different types of differential equations. An application of
the main theorem for Duffing equations is provided.Comment: 15 pages, 4 figure
The coalition myth
Coalition politics remains relatively unfamiliar to British politicians, despite the experience of the past five years. Throughout the election campaign, the main party leaders have poured scorn on the idea of another coalition after May 7th, and have given the public little detail on their preferences for different potential coalition partners. In this post, Marie-Noelle Loewe points to evidence from across Europe that suggests there is little reason to expect future coalitions to lead to chaos, incoherence, or unpredictable decision making
Exact solutions to chaotic and stochastic systems
We investigate functions that are exact solutions to chaotic dynamical
systems. A generalization of these functions can produce truly random numbers.
For the first time, we present solutions to random maps. This allows us to
check, analytically, some recent results about the complexity of random
dynamical systems. We confirm the result that a negative Lyapunov exponent does
not imply predictability in random systems. We test the effectiveness of
forecasting methods in distinguishing between chaotic and random time-series.
Using the explicit random functions, we can give explicit analytical formulas
for the output signal in some systems with stochastic resonance. We study the
influence of chaos on the stochastic resonance. We show, theoretically, the
existence of a new type of solitonic stochastic resonance, where the shape of
the kink is crucial. Using our models we can predict specific patterns in the
output signal of stochastic resonance systems.Comment: 31 pages, 18 figures (.eps). To appear in Chaos, March 200
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