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Towards the revival of oscillation from complete cessation in stochastic systems for application in molecular biology



Shakti Nath Singh1, Md. Zubbair Malik1* & RK Brojen Singh1



School of Computational & Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India;



RK Brojen Singh - brojen@jnu.ac.in; Md. Zubbair Malik - zubbairmalik@jnu.ac.in; *Corresponding Authors


Article Type

Research Article



Received December 12, 2019; Revised March 5, 2020, Accepted March 17, 2020; Published March 31, 2020



Delay and noise are inevitable in complex systems that are common in biochemical networks. The system is often disturbed at various states irrespective of the size (small or large) of delay and noise. Therefore, it is of interest to describe the significance of delay and noise in stochastic Willamowski-Rossler chemical oscillator model using a delay stochastic (having random probability distribution) simulation algorithm. Oscillating dynamics moves to stable fixed point when delay at a fixed magnitude of noise drives the system from oscillating state to stochastic amplitude death state (complete cessation). However, the amplitude death state is induced to a revived oscillating state in stochastic system (which is far from equilibrium state) for noise with a fixed value of delay. Thus, significantly large and small noise induces the dynamics of the system to amplitude death state. Hence, we describe the interplay of delay and noise in stochastic systems for the proper and efficient functioning of the complex system that are frequent in biological networks.



Stochastic, Time delay, noise, oscillation, amplitude.



Singh et al. 16(3): 274-282 (2020)


Edited by

P Kangueane






Biomedical Informatics



This is an Open Access article which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. This is distributed under the terms of the Creative Commons Attribution License.