This ScDSC school is mainly pedagogical, aimed at bridging the gap between graduate, postgraduate level courses and research. The courses are intended to provide a basic introduction, and  to equip students and early-career researchers with a robust foundation in the theory and applications of nonlinear/complexity science. 

The specific objectives of the school are:

• To introduce the fundamental concepts of nonlinear dynamics, including phase space, bifurcations, chaos, limit cycles, and attractors, with an emphasis on conceptual clarity and mathematical rigor.

• To provide hands-on training in analytical and computational techniques used to study nonlinear systems, utilizing tools such as Python, XPPAUT.

• To bridge theory and practice by exploring interdisciplinary applications of nonlinear dynamics across physics, biology, engineering, economics, social science, and machine learning.

• To enhance research skills through exposure to current trends, open problems, and potential research directions in the field of nonlinear science.

• To promote interaction and mentorship with collaborative environment for knowledge sharing and innovation.

This school hopes to serve as a platform to inspire and empower the next generation of researchers in nonlinear science and its wide-ranging real-world applications. 

Event Concluded:

See related links and posts:

• Speakers List 1

• Speakers List 2

• LinkedIn Post 1

Please click here for registration  (Registration is closed as the event is concluded)

Last Date of Registration: June 07, 2025

Information of selected candidates: June 09, 2025

Event dates: June 23 -- July 11, 2025

The key topics which will be covered in the school are as following:

• Introduction to dynamical systems

• Stability analysis and Bifurcations

• Strange Attractors and its characterizations

• Chaos and Complexity

• Time-Series Analysis

• Synchronization and Control

• Machine Learning and Dynamical Systems

• Nonlinear Stochastic Models of Social Systems

Detailed Syllabus:  Click Here To Download Full Syllabus

Basic Course – I (BC1) 12L

Introduction: Modeling the dynamical systems: examples and equation of motions, population models, Chemical Kinetics; Systems: Discrete vs continuous, linear vs nonlinear, conservative vs dissipative dynamical systems; Critical points (equilibria); classification of critical points: fixed points; Linear stability analysis; stable, unstable and center manifolds, Phase space analysis. [AP:5L, HJ:1L] Attractors: limit cycle, chaos; Characterization: Lyapunov exponent, sensitive dependence on initial conditions; Bifurcations: saddle-node, transcritical, pitchfork, and Hopf. [RR:5L, HJ:1L]

Basic Course – II (BC2) 12L

Discrete systems: shift, tent, logistic maps. Period doubling route to chaos, intermittency, invariant density; 2D maps: Baker, Cat maps, Image encryption using chaotic maps. [HJ: 3L, VP:2L] Coarse graining, fractals, generalized dimensions, Kolmogorov-Sinai entropy, correlation and information dimensions. Time series analysis, Attractor reconstruction. [MS:3L] Basic concepts of stochastic process, classification, stationary, Poisson Process, Markov Process, Random Walk. Diffusion equation, Introduction to SDE, Fokker – Plank equation, Master equation, System Size Expansion, Diffusion of Information in a Social Group, Nonlinear Models of Social Systems. [KU:4L]

Basic course –III (BC3) 8L

Hamiltonian Dynamics and Integrable Systems. Action-angle variables, Liouville integrability, quasi- periodicity, Poincare sections, invariant tori, etc. Symmetries, invariance and constant motion. Standard map, twist map, KAM theorem. Finite dimensional dynamical systems. [MS:4L] Introduction to Solitons: PDE(s), application to linear and nonlinear dispersive waves, solitary waves and solitons, NLS and Sine-Gordon equations, infinite number of constants of motion, complete integrability. [AP:4L]

Advanced Course - I: Synchronization and Control (SY-CO) 12L

Coupled Oscillators; types of interactions: instantaneous vs delay, similar vs conjugate; Emergent behavior due to coupling: synchronization, amplitude death, multistability, Chimera. [SU:4L] Synchronization: complete, phase, lag, generalized, intermittent; Nonlinear electronic circuits, Experimental demonstration of chaos and synchronization via electronic circuits. [UT:4L] Feedback Control Methods: linear and nonlinear control, robust and adaptive control, Lyapunov function and dissipativity-based methods [VC:4L]

Advanced Course – II: Network Science and Machine Learning (NS-ML) 12L

Network Science: Introduction to graph theory, types of graphs - regular and random networks, scale free networks, small world networks, network properties: degree distributions, clustering, centralities measures. Applications in physics, biology, technology and social networks etc. [NP:4L] Machine Learning: Artificial neural network, Hopfield network as dynamical system, Chaotic neural network, Feedforward and recurrent neural networks, Regression methods, data-driven dynamical systems, Machine Learning -- by Dynamical Systems, and -- for Dynamical Systems, Reservoir Computing, Neuromorphic computing.

Computer and Electronics Laboratory Experiments: (24L)

Basic programming and numerical methods/tools for dynamical systems, bifurcation analysis using XPP AUT, Imagining the Bacteria as a Dynamical System and other applications, Multisim, Electronic circuit experiments, etc, Introduction to network analysis using network, machine learning algorithm for predictions and control of dynamical systems. [PP, SS, HJ, SU, UT, NP, SD]

Course Instructors:

RR: Ram Ramaswamy, IISER Berhampur

MS: M S Santhanam, IISER Pune

AP: Awadesh Prasad, University of Delhi

MD: Manish Shrimali, CURaj

UT: Umeshkanta S. Thounaojam, Bennett University

NP: Nirmal Punetha, Amity University Haryana

SU: Sangeeta Ujjwal, BHU

HJ: Haider Hasan Jafri, AMU

SD: Shiva Dixit, Amity University Haryana

KU: Karmeshu, UPES 

VC: Vijaysekhar Chellaboina, UPES

VP: Vinod Patidar, UPES

PP: Parth Pratim Pandey, UPES

SS: Suchetana Sadhukhan, UPES

Click Here to download Full list of Selected Candidates

How to reach UPES?
(Travel information to University of Petroleum and Energy Studies (UPES), Bidholi Campus, Dehradun will be updated soon. Basic information is given below)

✈️ By Air:
Nearest Airport: Jolly Grant Airport, Dehradun
Distance: Approximately 45–48 km from Bidholi campus
Travel Time: Around 1.5 to 2 hours by taxi
Note: Taxis are readily available at the airport for direct travel to the campus.

🚂 By Train
Nearest Station: Dehradun Railway Station
Distance: Approximately 17–18 km from Bidholi campus
Travel Time: Around 45 minutes to 1 hour by auto-rickshaw or taxi
Tip: Prepaid auto-rickshaw and taxi services are available at the station.

🚌 By Bus
Nearest Bus Terminal: ISBT Dehradun
Distance: Approximately 20–23 km from Bidholi campus
Travel Time: Around 1 to 1.5 hours by local transport
Options: Taxi, local buses and shared auto-rickshaws are available.

In campus accommodation will be provided to the participants on sharing basis @ UPES Bidholi campus Dehradun. Food is also included. 

scdsc2025.UPES@gmail.com