Explore the mathematical foundations and real-world applications of tipping points in complex systems through this comprehensive lecture series from the International Centre for Theoretical Sciences. Delve into dynamical systems theory and learn how systems can undergo sudden, irreversible changes when pushed beyond critical thresholds. Master the fundamentals of stochastic dynamics, delay dynamical systems, and spatial systems while discovering early warning signals that can predict impending tipping points. Examine diverse applications across multiple disciplines including ecosystem dynamics, climate science, gene regulatory networks, human-environment interactions, and disease spread patterns. Study specific case studies ranging from savanna-woodland transitions and forest resilience in Northeast India to COVID-19 wave predictions and Indian monsoon rainfall patterns. Gain insights into cutting-edge research on rate-induced tipping, machine learning approaches for predicting critical transitions, and the operationalization of resilience for decision-making. Learn from leading experts as they present both theoretical frameworks and practical tools for understanding when and where early warning signals emerge in multi-species systems, thermoacoustic systems, and coupled human-environment systems.

Syllabus

Dynamical Systems and Tipping (Lecture 1) by Partha Sharathi Dutta
Dynamical Systems and Tipping (Lecture 2) by Partha Sharathi Dutta
Early Warning Signals by Partha Sharathi Dutta
Stochastic Dynamics (Lecture 1) by Sudipta Kumar Sinha
Stochastic Dynamics (Lecture 2) by Sudipta Kumar Sinha
Stochastic Dynamics (Lecture 3) by Sudipta Kumar Sinha
Delay Dynamical Systems (Lecture 1) by Debabrata Biswas
Tipping in Spatial Systems (Lecture 1) by Vishwesha Guttal
Tipping in Spatial Systems (Lecture 3) by Vishwesha Guttal
Delay Dynamical Systems (Lecture 2) by Debabrata Biswas
Tipping in Spatial Systems (Lecture 4) by Vishwesha Guttal
When and Where can we Expect to see Early Warning Signals in Multi-Species Systems...by Karen Abbott
Scaling and Potentiality in Tipping Point Analysis by Valeria Livina
Role of Trait Variation in Savanna-woodland Bistable System by Tanveen Randhawa
Stochastic Tipping Points in Optimal Tumor Evasion and Adaptation Induced....by Jason George
Linear and Nonlinear Vegetation Change by Sumanta Bagchi
How do we Operationalise Resilience for Decision Making by Vasilis Dakos
Timeline to Collapse by Francesco Cerini
Impact of Seasonality on Bi-stable Ecosystem Dynamics by Shuaib Palathingal
Harnessing the Universality of Tipping Points to Improve Early Warning Signal... by Chris Bauch
Evading Tippings in Spatial Ecosystems by Swarnendu Banerjee
Dynamics of a Slow-Fast Predator-Prey Model with a Predator-Dependent...by Pranali Roy Chowdhury
Anticipating Response Function in Gene Regulatory Networks by Pankaj Gautam
Examining Ecosystem Resilience of Forests in Northeast India...by Krishnapriya Tamma
Climate Tipping Points by Tim Lenton
Tipping Points in Coupled Human-environment Systems by Madhur Anand
Hyperexponential Growth and Log-periodicity Precede Extreme COVID-19 Waves by Induja Pavithran
Dynamical and Statistical Models of Indian Monsoon Rainfall by Amit Apte
Stochastic Analysis and Applications in Gene Networks by Chunhe Li
Rate-Induced Tipping in Asymptotically Autonomous Dynamical Systems: Theory.. by Sebastian Wieczorek
Imprints of log-periodicity and the prediction to blowout in a turbulent .... by Ankan Banerjee
Some new Research on Climate Tipping Points by Peter Cox
Machine learning methods trained on simple models can predict critical transitions... by Smita Deb
Tipping in Thermoacoustic Systems and Their Early Warning Signals by R. I. Sujith
Tipping in Spatial Systems (Lecture 2) by Vishwesha Guttal
Simple Examples of Rate and Bifurcation Tipping by Sebastian Wieczorek
How do We Operationalise Resilience for Decision-Making? by Vasilis Dakos
Critical rates of climate warming and abrupt collapse of ecosystems by Taranjot Kaur
A Gentle Introduction to Machine Learning (Lecture 1) by Narayanan Krishnan
A Gentle Introduction to Machine Learning (Lecture 2) by Narayanan Krishnan