Complex dynamics in hard oscillators: the influence of constant inputs

TL;DR

This paper investigates how constant external inputs influence the complex dynamics and bifurcations of radial isochron clocks with hard excitation, relevant for modeling biological systems with multiple stable states.

Contribution

It characterizes the local and global bifurcations, including saddle node on limit cycle bifurcations, in systems with coexisting attractors under external inputs.

Findings

Identification of saddle node on limit cycle bifurcations.

Analysis of how external inputs affect system stability.

Insights into complex dynamics of biological oscillators.

Abstract

Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several deterministic models based on systems of nonlinear ordinary differential equations have been proposed. Few studies have been developed to characterize how either an external input or the coupling can drive systems with different coexisting states. For the sake of simplicity, in this manuscript we focus on systems belonging to the class of radial isochron clocks that exhibits hard excitation, in order to investigate their complex dynamics, local and global bifurcations arising in presence of constant external inputs. In particular the occurrence of saddle node on limit cycle bifurcations is detected.