Two different modes of oscillation in a gene transcription regulatory network with interlinked positive and negative feedback loops

We study the oscillatory behaviour of a gene regulatory network with interlinked positive and negative feedback loop. Frequency and amplitude are two important properties of oscillation. Studied network produces two different modes of oscillation. In one mode (mode 1) frequency remains constant over a wide range amplitude and in other mode (mode 2) the amplitude of oscillation remains constant over a wide range of frequency. Our study reproduces both features of oscillations in a single gene regulatory network and show that the negative plus positive feedback loops in gene regulatory network offer additional advantage. We identified the key parameters/variables responsible for different modes of oscillation. The network is flexible in switching between different modes by choosing appropriately the required parameters/variables.