Abstract
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.
Highlights
Functional organization and regulation in biochemical systems are the outcome of chain of molecular interactions/events defined by sets of well-defined reactions in various pathways
Because of small population of molecular species participation in reaction channels of biological systems with random interactions among them exhibit randomness in the system [1]. These randomness and fluctuations become significant in case of very low molecular species population in the biological systems and to explain the dynamics of such systems we need to deal the mathematical models by considering the noise with stochastic modelling approach [1, 2]
Once the delay is switched on, the amplitudes and time periods of the and dynamics are decreased monotonically, the scenario, which can be known as stochastic amplitude death
Summary
Functional organization and regulation in biochemical systems are the outcome of chain of molecular interactions/events defined by sets of well-defined reactions in various pathways These molecular events in such systems occur in a certain random manner and needs to solve these sets of reactions to understand systems’ behaviour [1]. Because of small population of molecular species participation in reaction channels of biological systems with random interactions among them (random collisions among molecular species and random firing of reactions) exhibit randomness in the system [1] These randomness and fluctuations become significant in case of very low molecular species population in the biological systems and to explain the dynamics of such systems we need to deal the mathematical models by considering the noise with stochastic modelling approach [1, 2]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
