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View article: Templex for Lagrangian dynamics in the Southwestern Atlantic
Templex for Lagrangian dynamics in the Southwestern Atlantic Open
This work presents the first application of the templex approach to observational datasets, using Lagrangian trajectories obtained from satellite altimetry in the ocean. The templex is a recent topological construct that extends classical …
Topological fingerprinting of dynamical systems Open
Poincaré established a framework for understanding the dependence of a dynamical system's properties on its topology. Topological properties offer detailed insights into the fundamental mechanisms — stretching, squeezing, tearing, folding,…
A topological perspective on the wind-driven ocean circulation Open
We first present briefly recent insights on the effects of time-dependent forcing on systems with intrinsic variability, such as anthropogenic forcing on the climate system. These insights are applied next to the problem of periodic forcin…
View article: The Wind-Driven Double-Gyre Circulation: A topological characterization of attractors across regimes
The Wind-Driven Double-Gyre Circulation: A topological characterization of attractors across regimes Open
We use a quasi-geostrophic model of the wind-driven double-gyre to explore qualitative changes in the system's behavior through a novel topological framework called Templex. This method characterizes and classifies the system's attractors …
Topological modes of variability of the wind-driven ocean circulation Open
Templexes are topological objects that encode the branching organization of a flow in phase space. We build on these objects to introduce the concept of topological modes of variability (TMVs). TMVs are defined as dynamical manifestations …
A templex-based study of the Atlantic Meridional Overturning Circulation dynamics in idealized chaotic models Open
Significant changes in a system’s dynamics can be understood through modifications in the topological structure of its flow in phase space. In the Earth’s climate system, such changes are often referred to as tipping points. One of the lar…
Templex-based dynamical units for a taxonomy of chaos Open
Discriminating different types of chaos is still a very challenging topic, even for dissipative three-dimensional systems for which the most advanced tool is the template. Nevertheless, getting a template is, by definition, limited to thre…
Extreme events in a templex Open
Theoretical and numerical studies have shown that transient atmospheric motions leading to weather extremes can be classified through the instantaneous dimension and stability of a state of a dynamical system [Faranda et al., Sci. Rep., 20…
From the Rössler attractor to the templex Open
International audience
Review article: Dynamical systems, algebraic topology and the climate sciences Open
The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of this theo…
Random templex encodes topological tipping points in noise-driven chaotic dynamics Open
Random attractors are the time-evolving pullback attractors of deterministically chaotic and stochastically perturbed dynamical systems. These attractors have a structure that changes in time and that has been characterized recently using …
Reply on CC3 Open
Abstract. The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of…
Reply on RC2 Open
Abstract. The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of…
Reply on RC1 Open
Abstract. The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of…
Comment on egusphere-2023-216 Open
Abstract. The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of…
Reply to “Complimentary comment on egusphere-2023-216” CC1 & CC2 Open
Abstract. The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of…
Reply on CC1 Open
Abstract. The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of…
Complimentary comment on egusphere-2023-216 Open
Abstract. The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of…
Identifying topological tipping points in noise-driven chaotic dynamics using random templexes Open
Random attractors are the time-evolving pullback attractors of stochastically perturbed, deterministically chaotic dynamical systems. These attractors have a structure that changes in time, and that has been characterized recently using Br…
Review Article: Dynamical Systems, Algebraic Topology, and the Climate Sciences Open
The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of this theo…
Random templex encodes topological tipping points in noise-driven chaotic dynamics Open
Random attractors are the time-evolving pullback attractors of stochastically perturbed, deterministically chaotic dynamical systems. These attractors have a structure that changes in time, and that has been characterized recently using {\…
Flow-induced self-sustained oscillations in a straight channel with rigid walls and elastic supports Open
This work considers the two-dimensional flow field of an incompressible viscous fluid in a parallel-sided channel. In our study, one of the walls is fixed whereas the other one is elastically mounted, and sustained oscillations are induced…
Templex: A bridge between homologies and templates for chaotic attractors Open
The theory of homologies introduces cell complexes to provide an algebraic description of spaces up to topological equivalence. Attractors in state space can be studied using Branched Manifold Analysis through Homologies: this strategy con…
Early warning signals for topological tipping points Open
The topology of the branched manifold associated with the Lorenz models random attractor (LORA) evolves in time. LORAs time-evolving branched manifold robustly supports the point cloud associated with the systems invariant measure at each …
Noise-driven topological changes in chaotic dynamics Open
Noise modifies the behavior of chaotic systems in both quantitative and qualitative ways. To study these modifications, the present work compares the topological structure of the deterministic Lorenz (1963) attractor with its stochasticall…
Topological colouring of fluid particles unravels finite-time coherent sets Open
A Topological Reading of Ernesto Laclau Open
This work proposes a reading of Laclau’s theory on populism using concepts from topology applied to dynamical systems. The analogical correspondences are established between the elements used in the reconstruction of a topological structur…
Topological Effects of Noise on Nonlinear Dynamics Open
Noise modifies the behavior of chaotic systems. Algebraic topology sheds light on the most fundamental effects involved, as illustrated herein by using the Lorenz (1963) model. This model's attractor is "strange" but frozen in time. When d…
The Lorenz convection model's random attractor (LORA) and its robust topology Open
Chekroun et al. (Physica D, 240, 2011) studied the globalrandom attractor associatedwith the Lorenz (1963) model driven by multiplicative noise; they dubbed this time-evolving attractor LORA for short. The present talk examines the topolog…