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Chaos and Hyperchaos in a Model of Ribosome Autocatalytic Synthesis

Vitaly A. Likhoshvai, Vladislav V. Kogai, Stanislav I. Fadeev, Tamara M. Khlebodarova
2016 Scientific Reports  
In current work we present an elementary model in which the autocatalytic synthesis of ribosomal RNA and proteins, as well as enzymes ensuring their degradation are described with two monotonically increasing  ...  For certain parameter values, the model, consisting of one differential equation with delayed argument, demonstrates both stationary and oscillatory dynamics of the ribosomal protein synthesis, which can  ...  Acknowledgements The work of V.V.Kogai and S.I.Fadeev was supported by the RFBR (project 16-01-00237a), the work of T.M.Khlebodarova and V.A.Likhoshvai was supported by the Russian Science Foundation (  ... 
doi:10.1038/srep38870 pmid:27941909 pmcid:PMC5151018 fatcat:lb774dviyjfwhmuyo5zetdakri

Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays

Yoko Suzuki, Mingyang Lu, Eshel Ben-Jacob, José N. Onuchic
2016 Scientific Reports  
In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations  ...  Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays.  ...  Texas (CPRIT), and by the Tauber Family Funds and the Magut-Glass Chair in Physics of Complex Systems at Tel-Aviv University.  ... 
doi:10.1038/srep21037 pmid:26876008 pmcid:PMC4753448 fatcat:v6ybgowrsngublmb5qmqytu3ma

Chaos in time delay systems, an educational review [article]

Hendrik Wernecke, Bulcsú Sándor, Claudius Gros
2019 arXiv   pre-print
Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with it various kinds of chaotic phases.  ...  Several educational examples are included in addition as entry points to the rapidly developing field of time delay systems.  ...  W. thanks the organizers of the 675th Heraeus seminar on 'Delayed complex systems', Günter Radons, Andreas Otto, and Wolfram Just for an inspiring conference that facilitated the richness of topics in  ... 
arXiv:1901.04826v3 fatcat:fwfyma6tsfcjncnhsjjqgbvu3e

Bifurcation analysis of a first time-delay chaotic system

Tianzeng Li, Yu Wang, Xiaofeng Zhou
2019 Advances in Difference Equations  
This paper deals with the dynamic behavior of the chaotic nonlinear time delay systems of general formẋ(t) = g(x(t), x(t -τ )).  ...  Next, a numerical simulation of the prototype system is used to show that the system has different behaviors: stability, periodicity and chaos with the variation of delay and other parameters, which demonstrates  ...  Song et al. studied the stability and Hopf bifurcation in a model of gene expression with distributed time delays [31] .  ... 
doi:10.1186/s13662-019-2010-y fatcat:iwlivpa6xjaqfc4affkjne5d5i

A Review of Mathematical and Computational Methods in Cancer Dynamics [article]

Abicumaran Uthamacumaran, Hector Zenil
2022 arXiv   pre-print
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks.  ...  With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space  ...  Jacek Majewski of McGill University, for the knowledge he granted on glioma epigenetics and computational epigenetic modelling.  ... 
arXiv:2201.02055v5 fatcat:hxhvnvagcbdeldwsb3zet3wavu

A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

Abicumaran Uthamacumaran
2021 Patterns  
A toolbox of complex systems approaches are discussed for reconstructing the signaling state space of cancer networks, interpreting causal relationships in their time series gene expression patterns, and  ...  To overcome this burden, we must decipher the state-space attractor dynamics of gene expression patterns and protein oscillations orchestrated by cancer stemness networks.  ...  This article is dedicated to the innate systems thinkers [children] at the Glen Hospital, B7-Oncology (Montreal, QC) and their paintings, which have served as the greatest teachings of chaos, complexity  ... 
doi:10.1016/j.patter.2021.100226 pmid:33982021 pmcid:PMC8085613 fatcat:24cwwzxesfempbtmni4iz4cz5i

Chaos and physiology: deterministic chaos in excitable cell assemblies

T. Elbert, W. J. Ray, Z. J. Kowalik, J. E. Skinner, K. E. Graf, N. Birbaumer
1994 Physiological Reviews  
and negative feedback) and multiple feedback with different time constants are sources of chaos.  ...  Even in the context of feedback models, chaos would be expected in highly interconnected and tightly coupled feedback loops found in biosystems. 89, 91) found that systems with mixed feedback (both positive  ...  CHAOS AND PHYSIOLOGY 41 EEG.  ... 
doi:10.1152/physrev.1994.74.1.1 pmid:8295931 fatcat:pepxhusq4fd7tasrnoo3zcg2cy

Stochastic analysis of nonlinear dynamics and feedback control for gene regulatory networks with applications to synthetic biology

Natalja Strelkowa, Mauricio Barahona, The Wellcome Trust
2011
The algorithm operates model-free, i.e. in principle it is applicable to any genetic network and the input information is a data matrix of measured time series from the network dynamics.  ...  Also the length and distribution of quasi-stable oscillations are obtained. The findings suggest that long-lived transient dynamics due to feedback loops can dominate gene network dynamics.  ...  The study focuses on investigation of chaos and hyperchaos in the unidirectionally and linearly coupled oscillator system.  ... 
doi:10.25560/6405 fatcat:jotizan3wrfhngwkns5ivby5oa

Unscented approaches to inference and design for systems and synthetic biology

Daniel Silk, Michael Stumpf, Biotechnology And Biological Sciences Research Council (Great Britain)
2014
, such as oscillations, chaos and hyperchaos.  ...  In particular, the high dimensionality and complexity of biological systems along with significant experimental noise, means that tasks such as parameter fitting and model selection often require far more  ...  , such as oscillations, chaos and hyperchaos.  ... 
doi:10.25560/18393 fatcat:suorgof7mbgypef2ia32hcdcom