Marching bifurcations

This paper dedicated to my late mum and dad (Ludwika and Karol Wiercigroch), presents a light-hearted account of important events in my academic career, which have influenced my development and contributed to my achievements. It meant to be published on the occasion of my round birthday, which celebration was delayed by COVID-19 pandemic and some other factors. Predominantly, it is based on a booklet I wrote in 2013 on the occasion of bestowing on me a title a doctor honoris causa by the Technical University of Lodz (LUT) of my native Poland. The main focus of this piece is the friendship and interactions with my academic colleagues around the world and in particular with Professor Tomasz Kapitaniak of the LUT. In mathematics, a bifurcation is a qualitative change in a solution, wherein a march is not only a synonym of a periodic excitation but also the passing time. In this context, a bifurcation being a qualitative change has a major influence on the global solution. This definition resonates well a much wider context and this paper attempts to provide some examples.