Delay-induced chaos in coupled nonlinear regulatory systems: a mitotic checkpoint model

Abstract We study a delay differential equation model describing the nonlinear dynamics of two coupled regulatory modules motivated by spindle assembly and spindle position checkpoints. Biologically constrained time delays, representing feedback inhibition, phosphorylation cascades, and signal transport, are incorporated explicitly into the governing equations. These delays fundamentally modify the system’s phase space, leading to multistability, delay-induced oscillations, and deterministic chaos that do not arise in corresponding ordinary differential equation models. For sufficiently strong coupling and incommensurate delays, numerical simulations exhibit chaotic dynamics consistent with a positive largest Lyapunov exponent and strange-attractor-like phase structure. Bifurcation analysis reveals transitions between steady, oscillatory, and chaotic regimes organized by delay-dependent instabilities. The influence of stochastic perturbations is also examined, revealing a noise-induced enhancement of dynamical coherence consistent with stochastic resonance in delayed systems. Finally, several feedback-based control strategies are analyzed, demonstrating that smooth threshold modulation can effectively suppress chaos and restore regular dynamics. Together, these results highlight how explicit time delays act as fundamental drivers of complexity in nonlinear dynamical systems and provide a general framework for analyzing delay-induced phenomena in coupled regulatory networks.