DynamIC – Dynamical Systems at Imperial College London (DynamIC)

STAFF

	Jeroen Lamb
	Martin Rasmussen
	Dmitry Turaev
	Sebastian van Strien

HONORARY STAFF

POSTDOCS

PHD STUDENTS

Bernat Bassols-Cornudella

Matheus de Castro

Michal Fedorowicz

Vincent Goverse

Amir Khodaeian Karim

Leon Staresinic

Giuseppe Tenaglia

VISITORS

Cristina Sargent

RELATED STAFF

Mauricio Barahona

Davoud Cheraghi

DynamIC Seminars (Complete List)

Name	Title	Date	Time	Room
Juan Patino Echeverria (University of Auckland)	Transitions to wild chaos in a four-dimensional Lorenz-like systemAbstract: Wild chaos is a form of higher-dimensional chaotic dynamics that can only arise in vector fields of dimension at least four. This talk explores wild chaos in a four-dimensional system of differential equations, which is an extension of the classic Lorenz equations. Recently, Gonchenko, Kazakov and Turaev (2021) showed, via the computation of Lyapunov exponents, that this system has a wild chaotic attractor at a particular point in parameter space. To explain how this wild chaotic attractor arises geometrically, we perform a bifurcation analysis of the system in a two-parameter setting. As a starting point, we continue the one-parameter bifurcation structure of the classic Lorenz equations when the relevant new parameter is “switched on”. We find that the well-known homoclinic explosion point of the Lorenz system unfolds and gives rise to infinite cascades of curves of Shilnikov-type global connections in the four-dimensional system. These connections are formed by the unstable manifold of the origin, which plays an essential role in the emergence of complicated dynamics in the system. We also compute the kneading diagram that encodes how this one-dimensional manifold repeatedly moves around a pair of equilibria. In combination with the direct computation of curves of global bifurcations, the kneading diagram provides insight that helps identify regions where wild chaos may occur.	Tuesday, 4 June 2024	13:00	Huxley 140
Emmanuel Fleurentin (George Mason University and UNC Chapel Hill)	Investigating Most Probable Escape Paths over Periodic Boundaries: a Dynamical Systems ApproachAbstract: Noise-induced tipping (N-tipping) emerges when random fluctuations prompt transitions from one (meta)stable state to another, potentially as a rare event. In this talk, we delineate new techniques for determining Most Probable Escapes Paths (MPEPs) in stochastic differential equations over periodic boundaries. We utilize a dynamical system approach to unravel MPEPs for the intermediate noise regime. We discuss the framework for computing the MPEPs by first looking at intersections of stable and unstable manifolds of invariant sets of a Hamiltonian system derived from the Euler-Lagrange equations of the Freidlin-Wentzell (FW) functional. The Maslov index helps identify which critical points of the FW functional are local minimizers and assists in explaining the effects of the interaction of noise and the deterministic flow. The Onsager-Machlup functional, which is treated as a perturbation of the FW functional, will provide a selection mechanism to pick out the MPEP. We will illustrate our approach and compare our theoretical prediction with Monte Carlo simulations in the Inverted Van der Pol system and a carbon cycle model.	Tuesday, 18 June 2024	13:00	Huxley 140

DynamIC Workshops and Mini-Courses (Complete List)

Title	Date	Venue
CHAOS (Homoclinic Bifurcations, Strange Attractors, Arnold Diffusion, Fermi Acceleration, Solitons)	Sunday, 24 September 2023 – Friday, 29 September 2023	Nesin Math Village, Izmir, Turkey
Mini-Workshop on Heterodimensional Dynamics	Wednesday, 2 November 2022	Imperial College London

Short-term DynamIC Visitors (Complete List)

Name	Affiliation	Arrival	Departure	Host
No visitors scheduled currently

Links