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Nonlinear Effects in Site Blocking Induced Oscillations [article]

Dorjsuren Battogtokh, Ravjir Davaanyam
2003 arXiv   pre-print
Higher order nonlinear effects of site blocking, which induces oscillations in the Monte Carlo simulation of CO oxidation, are outlined here. It is shown that the rate equations which include these effects exhibit a supercritical Hopf bifurcation in parameter domains where Monte Carlo simulations lead to oscillations.
arXiv:cond-mat/0303019v1 fatcat:3g44ndhsnbgwtcilfg2j2w5yiu

Multiaffine Chemical Turbulence

Yoshiki Kuramoto, Dorjsuren Battogtokh, Hiroya Nakao
1998 Physical Review Letters  
A three-component reaction-diffusion model is proposed as the first example to exhibit chemical turbulence with multiaffine fractal structures, the underlying mechanism being the same as for similar turbulence discovered recently in some nonlocally coupled oscillator systems. The role played by the strongly diffusive component can be substituted by a long-wave random force, and this idea leads to our proposal of the second, far simpler reaction-diffusion model given by the randomly driven
more » ... gh-Nagumo nerve conduction equation. [S0031-9007(98)07376-1] PACS numbers: 82.20.Fd, 05.45. + b, 47.53. + n
doi:10.1103/physrevlett.81.3543 fatcat:uckibqqedfhgjlzp6d7jkagcle

Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators [article]

Yoshiki Kuramoto, Dorjsuren Battogtokh
2002 arXiv   pre-print
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into two domains, one composed of mutually synchronized oscillators with unique frequency and the other composed of desynchronized oscillators with distributed frequencies. We apply a theory similar to the one which successfully explained the onset of collective
more » ... ynchronization in globally coupled phase oscillators with frequency distribution. A space-dependent order parameter is thus introduced, and an exact functional self-consistency equation is derived for this quantity. Its numerical solution is confirmed to reproduce the simulation results accurately.
arXiv:cond-mat/0210694v1 fatcat:zvm7stjrf5gw5kw3xinuvqlwnq

Turbulence near cyclic fold bifurcations in birhythmic media

Dorjsuren Battogtokh, John J. Tyson
2004 Physical Review E  
We show that at the onset of a cyclic fold bifurcation, a birhythmic medium composed of glycolytic oscillators displays turbulent dynamics. By computing the largest Lyapunov exponent, the spatial correlation function, and the average transient lifetime, we classify it as a weak turbulence with transient nature. Virtual heterogeneities generating unstable fast oscillations are the mechanism of the transient turbulence. In the presence of wavenumber instability, unstable oscillations can be
more » ... cted leading to stationary turbulence. We also find similar turbulence in a cell cycle model. These findings suggest that weak turbulence may be universal in biochemical birhythmic media exhibiting cyclic fold bifurcations.
doi:10.1103/physreve.70.026212 pmid:15447570 fatcat:ho3myaqfpjgu3doqsmwl2wy6a4

Bifurcation analysis of a model of the budding yeast cell cycle

Dorjsuren Battogtokh, John J. Tyson
2004 Chaos  
We study the bifurcations of a set of nine nonlinear ordinary differential equations that describe regulation of the cyclin-dependent kinase that triggers DNA synthesis and mitosis in the budding yeast, Saccharomyces cerevisiae. We show that Clb2-dependent kinase exhibits bistability ͑stable steady states of high or low kinase activity͒. The transition from low to high Clb2-dependent kinase activity is driven by transient activation of Cln2-dependent kinase, and the reverse transition is driven
more » ... by transient activation of the Clb2 degradation machinery. We show that a four-variable model retains the main features of the nine-variable model. In a three-variable model exhibiting birhythmicity ͑two stable oscillatory states͒, we explore possible effects of extrinsic fluctuations on cell cycle progression. Most important events of the cell cycle-DNA synthesis, mitosis, and cell division-are regulated by a complex network of protein interactions that control the activities of cyclin-dependent protein kinases. The network can be modeled by a set of nonlinear differential equations, whose dynamics can be studied through numerical simu- lations. Bifurcation analysis is a mathematical tool which provides insights to numerical results. We illustrate this tool by comparing predictions from Chen's budding yeast cell cycle model to experiments carried out by Cross et al. †Mol. Biol. Cell. 13, 52 "2002... ‡, and by identifying reduced systems of equations retaining the main features of Chen's model. Bifurcation analysis also identifies a parameter region where cell cycle progression can be particularly sensitive to extrinsic fluctuations. D.; Tyson, J. J., "bifurcation analysis of a model of the budding yeast cell cycle," Chaos 14, 653 (2004); http://dx. Characteristic concentrations ͑dimensionless͒ ͓Cln3͔ max ϭ0.02 ͓Bck2͔ 0 ϭ0.0027 J d2,c1 ϭ0.05 J a,sbf ϭJ i,sbf ϭ0.01 J a,mcm ϭJ i,mcm ϭ1 J a,swi ϭJ i,swi ϭ0.1 J a,t1 ϭJ i,t1 ϭ0.05 Kinase efficiencies ͑dimensionless͒ ⑀ c1,n3 ϭ20 ⑀ c1,k2 ϭ2 ⑀ c1,b2 ϭ0.067 ⑀ c1,b5 ϭ1 ⑀ i,t1,n2 ϭ1 ⑀ i,t1,b2 ϭ1 ⑀ i,t1,b5 ϭ0.5 ⑀ sbf,n3 ϭ75 ⑀ sbf,b5 ϭ0.5 Other parameters f ϭ0.433 J n3 ϭ6 D n3 ϭ1 ϭ0.005 776
doi:10.1063/1.1780011 pmid:15446975 fatcat:kfq5hnjx7rgf3iamcqn3p7mvum

Deciphering the Dynamics of Interlocked Feedback Loops in a Model of the Mammalian Circadian Clock [article]

Dorjsuren Battogtokh, John J. Tyson
2018 bioRxiv   pre-print
Mathematical models of fundamental biological processes play an important role in consolidating theory and experiments, especially if they are systematically developed, thoroughly characterized, and well tested by experimental data. In this work, we report a detailed bifurcation analysis of a mathematical model of the mammalian circadian clock network developed by Relogio et al. [16], noteworthy for its consistency with available data. Using one- and two-parameter bifurcation diagrams, we
more » ... e how oscillations in the model depend on the expression levels of its constituent genes and the activities of their encoded proteins. These bifurcation diagrams allow us to decipher the dynamics of interlocked feedback loops, by parametric variation of genes and proteins in the model. Among other results, we find that REV-ERB, a member of a subfamily of orphan nuclear receptors, plays a critical role in the intertwined dynamics of Relogio's model. The bifurcation diagrams reported here can be used for predicting how the core-clock network responds - in terms of period, amplitude and phases of oscillations - to different perturbations.
doi:10.1101/306852 fatcat:wc52bsag4zamhoeisfqrecot7q

Analysis of a Generic Model of Eukaryotic Cell-Cycle Regulation

Attila Csikász-Nagy, Dorjsuren Battogtokh, Katherine C. Chen, Béla Novák, John J. Tyson
2006 Biophysical Journal  
Using a model similar to ours, Battogtokh and Tyson (34) showed that, for control systems operating close to a bifurcation to the stable M-like steady state, cells might get stuck in mitosis after a  ... 
doi:10.1529/biophysj.106.081240 pmid:16581849 pmcid:PMC1471857 fatcat:yj2sp7v2irfu3jnqe765qkdypa

A Bistable Switch Mechanism for Stem Cell Domain Nucleation in the Shoot Apical Meristem

Dorjsuren Battogtokh, John J. Tyson
2016 Frontiers in Plant Science  
The distance between the domains can be calculated from the model (Battogtokh, 2015) .  ...  Let us consider a bistable regime in the model and introduce a new diffusive variable, H, a hypothetical, rapidly diffusing hormone (Battogtokh, 2015) .  ...  Copyright © 2016 Battogtokh and Tyson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY).  ... 
doi:10.3389/fpls.2016.00674 pmid:27242874 pmcid:PMC4876614 fatcat:4xcghxrctfbibe7hfc2rmohns4

Mean-Field Theory Revives in Self-Oscillatory Fields with Non-Local Coupling

Yoshiki Kuramoto, Shin-ichiro Shima, Dorjsuren Battogtokh, Yuri Shiogai
2006 Progress of Theoretical Physics Supplement  
The existence of such pattern was first confirmed and explained by Kuramoto and Battogtokh 7) for a one-dimensional array of phase oscillators, and studied in further detail by Abrams and Strogatz who  ...  The existence of this peculiar state was first noticed by Battogtokh 15) while doing a numerical analysis of a simple non-locally coupled phase oscillator model of the form ∂ ∂t φ(x, t) = ω − K ∫ dx  ... 
doi:10.1143/ptps.161.127 fatcat:ru5les23vrga3mp6g3lkldmvom

Modeling the interactions of sense and antisense Period transcripts in the mammalian circadian clock network

Dorjsuren Battogtokh, Shihoko Kojima, John J. Tyson, Joerg Stelling
2018 PLoS Computational Biology  
Author Contributions Conceptualization: Dorjsuren Battogtokh, Shihoko Kojima, John J. Tyson.  ... 
doi:10.1371/journal.pcbi.1005957 pmid:29447160 pmcid:PMC5831635 fatcat:nm3b5clbcbcxrilg27qz4otoru

Domain nucleation and confinement in agent-controlled bistable systems

Dorjsuren Battogtokh
2015 Physical Review E  
We report a new mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et. al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules immersed in the medium of a fast diffusive agent. Here we show that, as the system grows, a new domain nucleates spontaneously in the area where the local level of the agent becomes critical. Newly nucleated domains are stable and the pattern formation is different
more » ... rom Turing's mechanism in monostable systems. Domains are spatially confined by the agent even if the activator and inhibitor molecules diffuse. With the spatial extension of the system, a larger domain may undergo a wavenumber instability and the concentrations of active molecules within the neighboring elements of a domain can become sharply different. The new mechanism reported in this work can be generic for pattern formation systems involving multistability, growth, and indirect coupling.
doi:10.1103/physreve.91.032713 pmid:25871150 fatcat:wsarqypctzaoji75vtfzdxbikm

Comparison of Domain Nucleation Mechanisms in a Minimal Model of Shoot Apical Meristem [article]

Dorjsuren Battogtokh, John J. Tyson
2017 arXiv   pre-print
Existing mathematical models of the shoot apical meristem (SAM) explain nucleation and confinement of a stem cell domain by Turing's mechanism, assuming that the diffusion coefficients of the activator (WUSCHEL) and inhibitor (CLAVATA) are significantly different. As there is no evidence for this assumption of differential diffusivity, we recently proposed a new mechanism based on a bistable switch model of the SAM. Here we study the bistable-switch mechanism in detail, demonstrating that it
more » ... be understood as localized switches of WUSHEL activity in individual cells driven by a non-uniform field of a peptide hormone. By comparing domain formation by Turing and bistable-switch mechanisms on a cell network, we show that the latter does not require the assumptions needed by the former, which are not supported by biological evidences.
arXiv:1604.04643v3 fatcat:4ipcx66herfbjjbne5lokgkxsy

Morphological plant modeling: Unleashing geometric and topological potential within the plant sciences [article]

Alexander Bucksch, Acheampong Atta-Boateng, Akomian Fortune Azihou, Mathilde Balduzzi, Dorjsuren Battogtokh, Aly Baumgartner, Brad Binder, Siobhan Braybrook, Cynthia Chang, Viktoriya Coneva, Thomas DeWitt, Alexander Fletcher (+26 others)
2016 bioRxiv   pre-print
Plant morphology is inherently mathematical in that morphology describes plant form and architecture with geometrical and topological descriptors. The geometries and topologies of leaves, flowers, roots, shoots and their spatial arrangements have fascinated plant biologists and mathematicians alike. Beyond providing aesthetic inspiration, quantifying plant morphology has become pressing in an era of climate change and a growing human population. Modifying plant morphology, through molecular
more » ... ogy and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems with fewer natural resources. In this white paper, we begin with an overview of the mathematical models applied to quantify patterning in plants. We then explore fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leafs in air streams. We end with a discussion concerning the incorporation of plant morphology into educational programs. This strategy focuses on synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. This white paper arose from bringing mathematicians and biologists together at the National Institute for Mathematical and Biological Synthesis (NIMBioS) workshop titled Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences held at the University of Tennessee, Knoxville in September, 2015. Never has the need to quantify plant morphology been more imperative. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.
doi:10.1101/078832 fatcat:u4sfyb4ctjeizfmfbshryu3xnq

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

Alexander Bucksch, Acheampong Atta-Boateng, Akomian F. Azihou, Dorjsuren Battogtokh, Aly Baumgartner, Brad M. Binder, Siobhan A. Braybrook, Cynthia Chang, Viktoirya Coneva, Thomas J. DeWitt, Alexander G. Fletcher, Malia A. Gehan (+25 others)
2017 Frontiers in Plant Science  
At the molecular scale, models can treat some biomolecules as diffusive, but others, such as membrane-bound receptors, can be spatially restricted (Battogtokh and Tyson, 2016) .  ... 
doi:10.3389/fpls.2017.00900 pmid:28659934 pmcid:PMC5465304 fatcat:uw442um6rnfhvpdeqckysmllba
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