Thank you for the reply. I am using the ruler as an informal way of introducing a Pitchfork Bifurcation—see [3]. Although the specific analogy to a ruler may appear tenuous, my article merely attempts to draw links between the underlying dynamics, in which a stable point (with symmetries) splits into two stable branches protruding from a critical point. This setup is used to study a wide variety of physical and biological phenomena—see [Catastrophe Theory and its Applications, Poston and Stewart, 1978].
Thank you for the reply. I am using the ruler as an informal way of introducing a Pitchfork Bifurcation—see [3]. Although the specific analogy to a ruler may appear tenuous, my article merely attempts to draw links between the underlying dynamics, in which a stable point (with symmetries) splits into two stable branches protruding from a critical point. This setup is used to study a wide variety of physical and biological phenomena—see [Catastrophe Theory and its Applications, Poston and Stewart, 1978].