Multicluster splitting and bursting transients in mean-field coupled logistic delay networks

Abstract We study a network of identical logistic delay oscillators coupled through a mean field and focus on how the interplay of intrinsic delay and global coupling organizes collective dynamics, with emphasis on multicluster splitting and bursting transients. For a pair of coupled oscillators, we derive an estimate for the coupling threshold for complete synchronization, which provides a baseline coupling scale for the network. Extending to large networks, we map dynamical regimes in the $$(\epsilon ,\tau )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϵ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> plane and characterize the transitions using spatiotemporal patterns and a strength-of-incoherence measure. In the periodic regime, increasing delay induces a period-doubling route that manifests as successive splitting of coherent multicluster states. For larger delays, the clustered motion loses stability through intermittency: long laminar intervals with low-frequency square-wave-like oscillations are punctuated by localized chaotic bursts that widen in time and ultimately lead to spatiotemporal chaos. Our results highlight the competing roles of mean-field coupling (stabilizing coherence) and delay (driving bifurcations and intermittency) in shaping the transient and long-time behavior of logistic delay networks.