3,187 research outputs found
Chaos in the motion of a test scalar particle coupling to Einstein tensor in Schwarzschild-Melvin black hole spacetime
We present firstly the equation of motion for a test scalar particle coupling
to Einstein tensor in the Schwarzschild-Melvin black hole spacetime through the
short-wave approximation. Through analysing Poincar\'{e} sections, the power
spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram, we
investigate the effects of coupling parameter on the chaotic behavior of the
particles. With the increase of the coupling strength, we find that the motion
of coupled particle for the chosen parameters becomes more regular and order
for the negative couple constant. While, for the positive one, the motion of
coupled particles first undergoes a series of transitions between chaotic
motion and regular motion and then falls into horizon or escapes to spatial
infinite. Our results show that the coupling brings about richer effects for
the motion of the particles.Comment: 18 pages, 9 figures. The title is changed, some content and
references are modified. Accepted by EPJC for publication;arXiv admin note:
text overlap with arXiv:1604.0278
E&F Chaos: a user friendly software package for nonlinear economic dynamics
The use of nonlinear dynamic models in economics and finance has expanded rapidly in the last two decades. Numerical simulation is crucial in the investigation of nonlinear systems. E&F Chaos is an easy-to-use and freely available software package for simulation of nonlinear dynamic models to investigate stability of steady states and the presence of periodic orbits and chaos by standard numerical simulation techniques such as time series, phase plots, bifurcation diagrams, Lyapunov exponent plots, basin boundary plots and graphical analysis. The package contains many well-known nonlinear models, including applications in economics and finance, and is easy to use for non-specialists. New models and extensions or variations are easy to implement within the software package without the use of a compiler or other software. The software is demonstrated by investigating the dynamical behavior of some simple examples of the familiar cobweb model, including an extension with heterogeneous agents and asynchronous updating of strategies. Simulations with the E&F chaos software quickly provide information about local and global dynamics and easily lead to challenging questions for further mathematical analysis.
Li–Yorke chaos in nonautonomous Hopf bifurcation patterns - I
We analyze the characteristics of the global attractor of a type of
dissipative nonautonomous dynamical systems
in terms of the Sacker and Sell spectrum of its linear part.
The model gives rise to a pattern of nonautonomous Hopf bifurcation
which can be understood as a generalization of the classical autonomous one.
We pay special attention to the dynamics at the bifurcation point,
showing the possibility of occurrence of Li-Yorke chaos in the
corresponding attractor and hence of a high degree of unpredictability.MINECO/FEDER, MTM2015-66330-PEuropean Commission, H2020-MSCA-ITN-201
Bifurcations in the Lozi map
We study the presence in the Lozi map of a type of abrupt order-to-order and
order-to-chaos transitions which are mediated by an attractor made of a
continuum of neutrally stable limit cycles, all with the same period.Comment: 17 pages, 12 figure
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