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Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…
This paper addresses the amplitude and phase dynamics of a large system non-linear coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the…
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…
The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would…
Intracellular transmission of information via chemical and transcriptional networks is thwarted by a physical limitation: the finite copy number of the constituent chemical species introduces unavoidable intrinsic noise. Here we provide a…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We study the dynamics of intracellular calcium oscillations in the presence of proteins that bind calcium on multiple sites and that are generally believed to act as passive calcium buffers in cells. We find that multisite calcium-binding…
We show that a ring of phase oscillators coupled with transmission delays can be used as a pattern recognition system. The introduced model encodes patterns as stable periodic orbits. We present a detailed analysis of the underlying…
Biological information processing as implemented by regulatory and signaling networks in living cells requires sufficient specificity of molecular interaction to distinguish signals from one another, but much of regulation and signaling…
This paper presents a new method for evaluating the synchronization of quasi-periodic oscillations of two oscillators, termed "chimeric synchronization". The family of metrics is proposed to create a neural network information converter…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
Adaptation of the chemotaxis sensory pathway of the bacterium Escherichia coli is integral for detecting chemicals over a wide range of background concentrations, ultimately allowing cells to swim towards sources of attractant and away from…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
The collective behavior of biological oscillators has been recognized as an important problem for several decades, but its control has come into limelight only recently. Much of the focus for control has been on desynchronization of an…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
In this paper we use a continuous model to describe the development of a single cell lineage following the committal of stem cells. Three separate controls are implemented in the model, namely the proliferative control of stem cells, the…
Many biological processes display oscillatory behavior based on an approximately 24 hour internal timing system specific to each individual. One process of particular interest is gene expression, for which several circadian transcriptomic…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…