76 citations · 669 across the 27 of their papers we have counts for
10 papers · 1 filter
Computation of attractor dimension and maximal sums of Lyapunov exponents using polynomial optimization
Jeremy P Parker, David Goluskin
Two approaches are presented for computing upper bounds on Lyapunov exponents and their sums, and on the Lyapunov dimension, among all trajectories of a dynamical system governed b…
Computation of minimal periods for ordinary differential equations
Jeremy P. Parker, David Goluskin
A framework is presented for lower-bounding periods among periodic solutions to an autonomous dynamical system governed by ordinary differential equations. For a chosen dynamical s…
Convex computation of maximal Lyapunov exponents
Hans Oeri, David Goluskin
We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formula…
Minimum wave speeds in monostable reaction-diffusion equations: sharp bounds by polynomial optimization
Jason J. Bramburger, David Goluskin
Many monostable reaction-diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are…
Bounding extreme events in nonlinear dynamics using convex optimization
Giovanni Fantuzzi, David Goluskin
We study a convex optimization framework for bounding extreme events in nonlinear dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs). This fram…
Bounding extrema over global attractors using polynomial optimisation
David Goluskin
We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bo…
Bounds on mean energy in the Kuramoto-Sivashinsky equation computed using semidefinite programming
David Goluskin, Giovanni Fantuzzi
We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov fun…
Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems
Ian Tobasco, David Goluskin, Charles R. Doering
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories,…
Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system
David Goluskin
We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain pro…
Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization
Giovanni Fantuzzi, David Goluskin, Deqing Huang +1
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynami…