American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Generalizations of Naismith's problem: Minimal transit time between two points in a heterogenous terrian
  • PROC Home
  • This Issue
  • Next Article
    Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations
2011, 2011(Special): 1404-1412. doi: 10.3934/proc.2011.2011.1404

Wavelet analysis of phase clusters in a distributed biochemical system

Andrey Yu. Verisokin 1, , Darya V. Verveyko 1, , Eugene B. Postnikov 1, and  Anastasia I. Lavrova 2,

1. 

Department of Theoretical Physics, Kursk State University, Radishcheva st., 33, 305000, Kursk, Russian Federation, Russian Federation, Russian Federation
2. 

Institute of Physics, Humboldt-University at Berlin, Newtonstr. 15, 12489, Berlin, Germany

Received  July 2010 Revised  March 2011 Published  October 2011

The spatio-temporal dynamics of glycolysis in distributed medium have been studied both theoretically and experimentally. Different patterns such as travelling waves, standing waves and clusters have been observed in experiment. We describe pattern formation using distributed Selkov model that describes kinetics of phosphofructokinase which is a key enzyme of glycolytic reactions. We have found in numerical simulations that the varying the diffusion coefficient values within the range of 0−10$^$−$^$3 shows a large variety of phase patterns: from the birth of a hierarchy of phase clusters to their complete phase synchronization. In order to understand the mechanism phase clusters emergence and their dynamics we are using continuous wavelet transform.
Keywords: glycolytic reaction, nonlinear oscillator, non-Turing bifurcations, distributed Selkov system, reaction-diffusion.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Andrey Yu. Verisokin, Darya V. Verveyko, Eugene B. Postnikov, Anastasia I. Lavrova. Wavelet analysis of phase clusters in a distributed biochemical system. Conference Publications, 2011, 2011 (Special) : 1404-1412. doi: 10.3934/proc.2011.2011.1404
[1]

Qi An, Weihua Jiang. Spatiotemporal attractors generated by the Turing-Hopf bifurcation in a time-delayed reaction-diffusion system. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 487-510. doi: 10.3934/dcdsb.2018183
[2]

Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4963-4998. doi: 10.3934/dcdsb.2020321
[3]

Narcisa Apreutesei, Vitaly Volpert. Reaction-diffusion waves with nonlinear boundary conditions. Networks & Heterogeneous Media, 2013, 8 (1) : 23-35. doi: 10.3934/nhm.2013.8.23
[4]

Thomas I. Seidman. Interface conditions for a singular reaction-diffusion system. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 631-643. doi: 10.3934/dcdss.2009.2.631
[5]

Jifa Jiang, Junping Shi. Dynamics of a reaction-diffusion system of autocatalytic chemical reaction. Discrete & Continuous Dynamical Systems, 2008, 21 (1) : 245-258. doi: 10.3934/dcds.2008.21.245
[6]

Weihua Jiang, Xun Cao, Chuncheng Wang. Turing instability and pattern formations for reaction-diffusion systems on 2D bounded domain. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021085
[7]

Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero. Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term. Discrete & Continuous Dynamical Systems, 2014, 34 (10) : 4155-4182. doi: 10.3934/dcds.2014.34.4155
[8]

Zhenguo Bai, Tingting Zhao. Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4063-4085. doi: 10.3934/dcdsb.2018126
[9]

Sebastian Aniţa, William Edward Fitzgibbon, Michel Langlais. Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 805-822. doi: 10.3934/dcdsb.2009.11.805
[10]

Lili Du, Chunlai Mu, Zhaoyin Xiang. Global existence and blow-up to a reaction-diffusion system with nonlinear memory. Communications on Pure & Applied Analysis, 2005, 4 (4) : 721-733. doi: 10.3934/cpaa.2005.4.721
[11]

Perla El Kettani, Danielle Hilhorst, Kai Lee. A stochastic mass conserved reaction-diffusion equation with nonlinear diffusion. Discrete & Continuous Dynamical Systems, 2018, 38 (11) : 5615-5648. doi: 10.3934/dcds.2018246
[12]

Vladimir V. Chepyzhov, Mark I. Vishik. Trajectory attractor for reaction-diffusion system with diffusion coefficient vanishing in time. Discrete & Continuous Dynamical Systems, 2010, 27 (4) : 1493-1509. doi: 10.3934/dcds.2010.27.1493
[13]

Henri Berestycki, Nancy Rodríguez. A non-local bistable reaction-diffusion equation with a gap. Discrete & Continuous Dynamical Systems, 2017, 37 (2) : 685-723. doi: 10.3934/dcds.2017029
[14]

Hideki Murakawa. Fast reaction limit of reaction-diffusion systems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1047-1062. doi: 10.3934/dcdss.2020405
[15]

Sven Jarohs, Tobias Weth. Asymptotic symmetry for a class of nonlinear fractional reaction-diffusion equations. Discrete & Continuous Dynamical Systems, 2014, 34 (6) : 2581-2615. doi: 10.3934/dcds.2014.34.2581
[16]

Sze-Bi Hsu, Junping Shi, Feng-Bin Wang. Further studies of a reaction-diffusion system for an unstirred chemostat with internal storage. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3169-3189. doi: 10.3934/dcdsb.2014.19.3169
[17]

Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan. Determination of initial data for a reaction-diffusion system with variable coefficients. Discrete & Continuous Dynamical Systems, 2019, 39 (2) : 771-801. doi: 10.3934/dcds.2019032
[18]

Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227-238. doi: 10.3934/mbe.2005.2.227
[19]

José-Francisco Rodrigues, Lisa Santos. On a constrained reaction-diffusion system related to multiphase problems. Discrete & Continuous Dynamical Systems, 2009, 25 (1) : 299-319. doi: 10.3934/dcds.2009.25.299
[20]

W. E. Fitzgibbon, M. Langlais, J.J. Morgan. A reaction-diffusion system modeling direct and indirect transmission of diseases. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 893-910. doi: 10.3934/dcdsb.2004.4.893

 Impact Factor: 

Tools

Metrics

  • PDF downloads (35)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences