Ordinary Differential Equations and Dynamical Systems

By Gerald Teschl. 2012

1,286 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7527298b981b254656f1234d54741c17b200ca92

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Lior Yariv
2. Michael Niemeyer
3. Jan Peters
4. Amos Gropp
5. Stefan Bauer
6. Joseph Boudreau
7. Eric S. Swanson
8. Yaron Lipman

In Control and Systems Engineering

1. Niklas Pfister
2. Stefan Bauer
3. Jan Peters
4. Lior Yariv
5. Michael Niemeyer
6. Amos Gropp
7. Joseph Boudreau
8. Eric S. Swanson

In Geometry and Topology

1. Lior Yariv
2. Michael Niemeyer
3. Jan Peters
4. Amos Gropp
5. Joseph Boudreau
6. Eric S. Swanson
7. Yaron Lipman
8. Denny Borsboom

Citations in the corpus

• Identifying Causal Structure in Large-Scale Kinetic Systems (2018, background): “The theorem by Picard-Lindelöf guarantees the existence of a unique solution if fθ is uniformly Lipschitz [e.g., Sideris, 2014, Theorem 3.9].”
• Ordinary Differential Equations (2018, positive): “The existence of a solution to the integral equation (6) follows from an iteration procedure similar to the one used in the proof of Lemma 4.”
• Motor primitives in space and time via targeted gain modulation in cortical networks (2018, neutral): “As before, performance is limited by the accuracy with which one can construct target movements as linear combinations of existing primitives.”
• Occupancy Flow: 4D Reconstruction by Learning Particle Dynamics (2019, methodology): “The gradients of (9) and (10) can be efficiently obtained using the adjoint sensitivity method [12, 50] by solving a second augmented ODE backwards in time.”
• A Review of Modeling Bioelectrochemical Systems: Engineering and Statistical Aspects (2016, background): “A classical form of ODE is shown in Equation (1) [68]:”
• Implicit Geometric Regularization for Learning Shapes (2020, methodology): “To show that q ( t ) converges to v we will introduce a Liapunov function ; the existence of such a function implies the desired convergence using standard stability results from the theory of dynamical systems (Wiggins, 2003; Teschl, 2012).”
• Dimensions of Normal Personality as Networks in Search of Equilibrium: You Can't like Parties if you Don't like People (2012, background): “This definition of equilibrium is analogous to ‘attractors’ in the complex systems literature (e.g. Teschl, 2008).”