Degeneracy in neuronal bifurcation landscapes: equivalent bifurcation sequences across distinct parameter sets

Degeneracy—the capacity of structurally distinct systems to achieve similar functions—is a fundamental property of living organisms, enabling adaptability and resilience. Neurons can maintain stable activity patterns despite wide variability in ion channel expression, highlighting how distinct internal configurations can yield equivalent electrophysiological behaviors. However, it remains unclear how degeneracy manifests in the context of bifurcations, the critical transitions between activity regimes that underlie phenomena such as different firing patterns, seizures and depolarization block. Here, we investigate how different biophysical parameter sets can lead to equivalent bifurcation sequences. Using a minimal neuron model with three variable conductances, we systematically explore how changes in extracellular potassium—mimicking physiological and pathological conditions—affect neuronal dynamics. Our results reveal that neurons with distinct intrinsic properties can traverse the same bifurcation pathways, entering regimes of bursting, seizure-like activity, and depolarization block. Yet, the specific parameter set determines the sensitivity and thresholds for these transitions. This work clarifies how degeneracy extends to the dynamical landscape of neurons, with implications for understanding resilience and vulnerability in neural circuits.