Bifurcation is a phenomenon that occurs in dynamical systems when a small change in a parameter leads to a qualitative change in the system's behavior. In the field of biomathematics, bifurcation analysis has been applied to various biological systems to understand their behavior and dynamics. Here are a few real-life examples of bifurcation in biomathematics:

Population dynamics: Bifurcation analysis has been used to study the dynamics of population growth and extinction. For example, in predator-prey models, changes in the predation rate or other parameters can lead to the emergence of stable or unstable limit cycles, which represent cyclic behavior of predator and prey populations.

Neural oscillations: Bifurcation analysis has been applied to study the behavior of neural oscillations, such as those observed in brain activity. The neuronal dynamics can exhibit bifurcations, leading to transitions between different patterns of activity, such as stable states, oscillatory behavior, or chaotic dynamics.

Cardiac rhythms: Bifurcation analysis has been used to investigate the dynamics of cardiac rhythms. Changes in parameters related to ion channel conductances can induce bifurcations, leading to transitions between normal and abnormal cardiac rhythms, such as the onset of arrhythmias.

Immunology: Bifurcation analysis has been applied to study immune system dynamics. For example, in models of immune response to pathogens, changes in parameters related to immune cell activation or pathogen load can induce bifurcations, leading to the emergence of stable or unstable steady states, limit cycles, or complex oscillatory behavior.

Epidemiology: Bifurcation analysis has been used to study the spread of infectious diseases. Changes in parameters such as the transmission rate or the effectiveness of interventions can lead to bifurcations, resulting in the emergence or disappearance of epidemic outbreaks.

These are just a few examples of how bifurcation analysis has been applied in biomathematics to understand the behavior and dynamics of various biological systems. Bifurcation analysis helps reveal the critical points at which systems undergo qualitative changes, allowing researchers to gain insights into the underlying mechanisms and make predictions about system behavior under different conditions

Thanks @Yazen Alawaideh for your response

In ODE cellular models of cardiac electrophysiology, look for examples of early afterdepolarizations and cardiac alternans. These have been long investigated from the point of view of bifurcations.