Dynamical systems in arbitrary dimensions: A consistent generalisation of low-dimensional models

October 26, 2026; 7:30 pm (IST)

Abstract: Professor Ramaswamy has recently applied Clifford’s geometric algebra to generalise the well-known Stuart Landau system to arbitrary dimensions D > 2. This approach recognises the special symmetries of the two-dimensional case and retains this feature in all dimensions, revealing a rich geometric and dynamical structure of the general model. We obtain exact solutions and describe the dynamical attractors and their basins of attraction in all dimensions. Since the model has “D” dimensional rotational symmetry, we further study the dynamics of an ensemble of oscillators in higher dimensions with coupling chosen to either preserve or break this symmetry. The emergent collective states can have unusual dynamical behaviour such as partial synchronization (when only a subset of the variables coincide and oscillate) and partial oscillation death (when a subset of variables asymptote to different stationary values). Similar Clifford extensions of other limit cycle oscillator systems can be made, offering a consistent procedure for generalising dynamical systems to arbitrary dimensions.

​

Biography:  Professor Ram Ramaswamy is a distinguished scientist whose research spans nonlinear dynamics, chaos theory, statistical physics, and complex systems. His work has made important contributions to understanding the behaviour of nonlinear dynamical systems, particularly the control and synchronization of chaotic and stochastic systems. His research interests also extend to computational biology and the dynamics of biological systems. Prof. Ramaswamy served as a Professor at Jawaharlal Nehru University, New Delhi, from 1986 to 2018, and as Vice-Chancellor of the University of Hyderabad from 2011 to 2015. He also served as President of the Indian Academy of Sciences from 2016 to 2018. He is an elected Fellow of the World Academy of Sciences, the Indian National Science Academy, and the Indian Academy of Sciences.