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Sishu Shankar Muni

Sishu Shankar Muni staff profile picture

School of Fundamental Sciences
College of Sciences


Thesis Title
Globally resonant homoclinic tangencies.

Research Description
Globally resonant homoclinic tangencies. Dynamical systems are systems evolving with time according to a given rule. Those systems involve parameters and we observe a lot of different interesting phenomena by varying the parameters. Multistability is common in dynamical systems in which for specific parameter values we observe the coexistence of several attractors, but the mechanism behind the multistability is poorly understood. My project is based on investigating a new geometric mechanism for multistability in smooth discrete-time dynamical systems (smooth maps). The project involves a nice blend of both analytical and numerical techniques which I enjoy working on. The motivation for this new mechanism dates back to a classic theorem in the 1950s. We have established a new geometric mechanism of multistability and it was confirmed in case of the piecewise smooth map in which we obtain a coexistence of a lot of infinitely many stable states. It is found that a special homoclinic tangency is responsible for this phenomenon. Getting the parameter regions for which this phenomenon occurs is crucial as in this region we obtain the coexistence of infinitely many stable states. Our aim is to unfold this problem in a general setting in smooth maps.

Research Importance
There is a need to understand the mechanism behind multistability in dynamical systems which are poorly understood. The mechanism can be used and applied in many different fields where multistability is common like neuroscience, climate dynamics, social systems, and ecosystems.

Research Benefit
We think this can shed some light on understanding the chaotic dynamics of discrete dynamical systems. We believe this project will be useful in understanding multistability better in different disciplines of study.

Personal Description
I am from Odisha, India. I have completed my Bachelor's and Master's degree in Mathematics from the National Institute of Technology, Rourkela. My master's thesis was on "Synchronization aspects of star-connected identical Chua circuits". The PhD project looked really interesting and challenging when I discussed it with my supervisors and was closely related to the origins of chaos theory, which I was always interested to explore. My supervisors were keen to supervise me which brought me to Massey. I plan to continue as a researcher in dynamical systems in the future. My webpage: https://sites.google.com/view/phenosis

Dr David Simpson
Distinguished Professor Robert McLachlan