Dynamical Routes to Dissipative Scaling in Biological Oscillators

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Nonlinear oscillatory systems across physics, chemistry, and biology frequently transition to complex dynamics through well-known routes to chaos. These include period-doubling cascades, quasiperiodic torus breakdown, intermittency, mixed-mode oscillations, and period-adding structures. Understanding which dynamical routes dominate in biological oscillators—and how they relate to underlying dissipative scaling—remains an open question.

Using examples compiled from the Biological Feigenbaum Spectrum (BFS) dataset, this memorandum surveys representative biological systems exhibiting classical nonlinear routes to chaos. Period-doubling cascades appear consistently across neural, biochemical, sensory, and cellular signaling systems, suggesting that this mechanism appears to be the most systematically documented route to complex dynamics in biological oscillators. Additional examples demonstrate that alternative routes—including period-adding cascades, intermittency, mixed-mode oscillations, and torus bifurcations—also occur in biological contexts, although these are less uniformly documented.

Together with recent numerical results on dissipative scaling in driven open quantum systems, these observations suggest that biological oscillators share a common dynamical landscape with broader non-equilibrium physics. Period-doubling provides a dominant organizing structure, while additional routes illustrate the broader diversity of nonlinear transitions available to dissipative biological dynamics.

Keywords:

Nonlinear dynamics
Biological oscillators
Period-doubling cascade
Routes to chaos
Dissipative systems
Non-equilibrium dynamics
Biochemical oscillations
Neuronal dynamics
Complex dynamical systems
Chaos in biological systems