2024-07-12 –, If (1.1)
This talk is about Attractors.jl, the newest module of DynamicalSystems.jl. It is the result of two featured scientific articles, and implements several new cutting edge tools to study stability in dynamical systems. It goes beyond traditional continuation tools by focusing explicitly on multistability and global stability, concepts extremely relevant for modern applications of dynamical systems such as climate tipping points or power grid stability.
Attractors.jl is a Julia package (part of the DynamicalSystems.jl) focusing on finding attractors of dynamical systems and continuing them along a parameter axis. Attractor is a concept that generalizes established concepts such as "fixed point" and "steady state". Our approach with Attractors.jl was inspired by modern applications of dynamical systems: where multistability is crucial, and transitions between attractors (often termed as "tipping points") is one of the most important aspects of the system to understand.
That is why we designed Attractors.jl to be different than traditional "continuation" software. Our approach is like a "birds-eye-view" of the state space, instead of focusing locally on a particular point. This approach comes with two strong benefits: 1) multistability can be detected automatically, 2) stability of attractors is quantified in terms of more powerful and general concepts of global stability (versus the established standard concepts of local stability). Additionally, Attractors.jl has been designed so that its core interfaces are extendable out-of-the-box, allowing future progress in stability analysis to be directly integrated with the package!
In this talk we will discuss the following points:
- Introduction to multistable dynamical systems for a general audience (with some background in math or natural sciences)
- Overview of the features of Attractors.jl
- The importance of multistability and global stability in real-world applications of dynamical systems
- The interface(s) of Attractors.jl and their extendable design
- Comparison with traditional continuation software
- A runnable code snippet using the package
I am an applied physicist/mathematician with a broad interest in nonlinear dynamics and complex systems and their application to understand the physical world at a conceptual level. My main focus in my research is understanding the interaction of clouds, climate variability, and climate multistability. Besides research, I am the lead developer of the JuliaDynamics software organization, an advocate of open source code and good scientific code practices in academia, and passionate about teaching applied physics/mathematics with a fresh, hands-on computational style