Zobrazeno 1 - 10
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pro vyhledávání: '"37G35, 39A28"'
Autor:
Ghosh, Indranil, Simpson, David J. W.
We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions correspond to
Externí odkaz:
http://arxiv.org/abs/2410.22563
Autor:
Glendinning, P. A., Simpson, D. J. W.
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these phenomena
Externí odkaz:
http://arxiv.org/abs/2211.05917
Autor:
Simpson, David J. W.
In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a stable fixed point of a piecewise-smooth map collides with a switching
Externí odkaz:
http://arxiv.org/abs/2207.10251
Autor:
Ghosh, Indranil, Simpson, David J. W.
The collection of all non-degenerate, continuous, two-piece, piecewise-linear maps on $\mathbb{R}^2$ can be reduced to a four-parameter family known as the two-dimensional border-collision normal form. We prove that throughout an open region of param
Externí odkaz:
http://arxiv.org/abs/2111.12893
Autor:
Ghosh, Indranil, Simpson, David J. W.
We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on $\mathbb{R}^2$) in the robust chaos parameter region of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80
Externí odkaz:
http://arxiv.org/abs/2109.09242
Autor:
Glendinning, P. A., Simpson, D. J. W.
In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tangent space. If this approach fails it may be possible to adapt the strat
Externí odkaz:
http://arxiv.org/abs/2108.05999
As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We argue that this is not a helpful concept for smooth unimodal maps for
Externí odkaz:
http://arxiv.org/abs/1906.11974
Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we provide forma
Externí odkaz:
http://arxiv.org/abs/1906.11969
Autor:
Simpson, David J. W.
The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain structure with poi
Externí odkaz:
http://arxiv.org/abs/1510.01416
Autor:
P.A. Glendinning, D.J.W. Simpson
Publikováno v:
Applied Mathematics and Computation. 434:127357
In some maps the existence of an attractor with a positive Lyapunov exponent can be proved by constructing a trapping region in phase space and an invariant expanding cone in tangent space. If this approach fails it may be possible to adapt the strat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1345cb16b187ab9d47ed86bb86372276
https://doi.org/10.1016/j.amc.2022.127357
https://doi.org/10.1016/j.amc.2022.127357
