Singh Shakti Nath, Malik Md Zubbair, Singh Rk Brojen
School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
Bioinformation. 2020 Mar 31;16(3):274-282. doi: 10.6026/97320630016274. eCollection 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.
在生化网络中常见的复杂系统中，延迟和噪声是不可避免的。无论延迟和噪声的大小（小或大）如何，系统在各种状态下都会经常受到干扰。因此，使用延迟随机（具有随机概率分布）模拟算法来描述延迟和噪声在随机威廉姆斯基-罗斯勒化学振荡器模型中的意义是很有意义的。当在固定噪声幅度下的延迟将系统从振荡状态驱动到随机振幅死亡状态（完全停止）时，振荡动力学移动到稳定的固定点。然而，对于具有固定延迟值的噪声，在随机系统（远离平衡状态）中，振幅死亡状态会被诱导到恢复的振荡状态。因此，显著大的和小的噪声会使系统动力学进入振幅死亡状态。因此，我们描述了随机系统中延迟和噪声的相互作用，以确保生物网络中频繁出现的复杂系统能够正常、高效地运行。
