NIAS Wednesday Discussion: "Complex dynamics of the `simple' nonlinear pendulum" by Janaki Balakrishnan, Lecture Hall, NIAS, 0930 hrs

NIAS Wednesday Discussion

 

Complex dynamics of the `simple' nonlinear pendulum

                         

Speaker

Janaki Balakrishnan

Professor & Head, Complex Systems Programme,

School of Natural & Engineering Sciences, NIAS

janaki05@gmail.com  

                                   

Chairperson: Sudharsana V. Iyengar, Post-doctoral Research Associate, Complex Systems Programme, NIAS, sudhaeinstein@gmail.com       

28th June, 2017, 9.30 am, Lecture Hall, NIAS

 

Abstract: The simple nonlinear pendulum under different conditions remains no longer simple. In the literature it has been used to represent different nonlinear processes and as simplified models of different physical and biological systems. Its behaviour under damping and external forcing, though studied extensively over the years, continues to evoke immense interest because of the numerous unexplored modes of oscillation and dynamical behaviour it can exhibit.

In this talk we present an overview of some of our studies on the system and its variants. In particular we will also discuss the mechanical system of a driven pendulum with linear velocity damping, under constant torque and dynamic feedback. We report an interesting bow-tie shaped bursting oscillatory behaviour, which is exhibited for small driving frequencies, in a certain parameter regime, which has not been reported earlier in this system. Similar bursts of identical bow-tie shape have been reported by us previously in a system of two resistively coupled Josephson junctions in a certain parameter regime when one junction is kept in an oscillatory mode and the other in an excitable (shunted) mode. We show that the bursting oscillations are caused because of a transition of the quiescent state to the spiking state by a saddle-focus bifurcation, and because of another saddle-focus bifurcation, which leads to cessation of spiking, bringing the system back to the quiescent state. The resting period between two successive bursts is estimated analytically.

About the Speaker: Prof. Janaki Balakrishnan heads the Complex Systems Programme in the School of Natural Sciences & Engineering at NIAS, Bangalore. She has worked and published in a wide range of areas covering many diverse areas of physics including dynamical systems theory and its applications to physical, biological & real world problems. These include synchronization of neuronal activity, physics of sensory systems, bursting behaviour in nonlinear systems, bubble dynamics & acoustic cavitation, ecological modelling, impact of climate change on ecological dynamics, stochastic processes, quantum field theory in flat & curved spacetimes. She obtained her PhD in Theoretical High Energy Physics from the University of Delhi. She was an Associate Professor of Physics at the Central University of Hyderabad for several years before moving to Bangalore and has held visiting and other positions in various institutes in India and abroad.

All are cordially invited

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For further info, please contact Sangeetha Menon [prajnanata@gmail.com or smenon@nias.iisc.ernet.in] and D. Suba Chandran [subachandran@gmail.com], Coordinators of NIAS Wednesday Discussion Meetings, and NIAS Discussion Reports.

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Date: 
Wednesday, June 28, 2017