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pro vyhledávání: '"Parker, Jeremy"'
Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating equilibria in
Externí odkaz:
http://arxiv.org/abs/2411.10320
Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatio-temporal chaos and turbulence. Finding these UPOs is however notoriously difficult. Matrix-free loop convergence algorithms deform entire space-time fiel
Externí odkaz:
http://arxiv.org/abs/2409.03033
The Birman-Williams theorem gives a connection between the collection of unstable periodic orbits (UPOs) contained within a chaotic attractor and the topology of that attractor, for three-dimensional systems. In certain cases, the fractal dimension o
Externí odkaz:
http://arxiv.org/abs/2409.01719
Autor:
Parker, Jeremy P
We formulate, for continuous-time dynamical systems, a sufficient condition to be a gradient-like system, i.e. that all bounded trajectories approach stationary points and therefore that periodic orbits, chaotic attractors, etc. do not exist. This co
Externí odkaz:
http://arxiv.org/abs/2401.10649
It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic dissipative systems; analogous to sums over periodic orbits formalize
Externí odkaz:
http://arxiv.org/abs/2301.10626
Autor:
Parker, Jeremy P, Valva, Claire
The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical systems, it is po
Externí odkaz:
http://arxiv.org/abs/2211.17119
Autor:
Parker, Jeremy P, Schneider, Tobias M
One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional unstable fixed
Externí odkaz:
http://arxiv.org/abs/2207.05163
Autor:
Parker, Jeremy P, Schneider, Tobias M
Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equation
Externí odkaz:
http://arxiv.org/abs/2108.12219
Publikováno v:
Chaos 31, 103102 (2021)
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain inequalit
Externí odkaz:
http://arxiv.org/abs/2106.13518
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