Predicting Limit Cycle Boundaries Deep Inside Parameter Space of a 2D Biochemical Nonlinear Oscillator Using Renormalization Group

2021 ◽  
Vol 31 (11) ◽  
pp. 2150162
Author(s):  
Ayan Dutta ◽  
Jyotipriya Roy ◽  
Dhruba Banerjee
Keyword(s):  
Renormalization Group ◽  
Phase Space ◽  
Limit Cycle ◽  
Parameter Space ◽  
Nonlinear Oscillator ◽  
Nonlinear Oscillators ◽  
Bifurcation Curve ◽  
Recent Past ◽  
Perturbative Renormalization ◽  
Biochemical Oscillator

Formation and study of periodic orbits in phase space in the case of nonlinear oscillators have been a topic of much interest in the recent past. In the current work, a method to go deep inside the limit cycle zone on one side of the bifurcation curve of a 2D non-Lienard biochemical oscillator has been introduced. It is discussed how such an introduction facilitates predicting the boundaries of limit cycles at various points of parameter space, nearly accurately, by the use of perturbative Renormalization Group. Sel’kov model of Glycolytic oscillator has been chosen as the base model to introduce the method.

scholarly journals Lyapunov Stability and Attractors of Some Systems of Nonlinear Oscillators

1986 ◽  
Vol 41 (8) ◽  
pp. 987-988 ◽  
Author(s):  
H. Tasso
Keyword(s):  
Phase Space ◽  
Limit Cycle ◽  
Lyapunov Stability ◽  
Lyapunov Functions ◽  
Nonlinear Oscillators ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Single Oscillator

Lyapunov functions valid in the greater part of phase space were found for a system of nonlinear oscillators of an extended Van der Pol type. They yield a good estimate of the location of attractors. For a particular single oscillator the appropriately modified Van der Pol equation delivers an ellipse as limit cycle.

scholarly journals RECURRING ANTI-PHASE SIGNALS IN COUPLED NONLINEAR OSCILLATORS: CHAOTIC OR RANDOM TIME SERIES?

1993 ◽  
Vol 03 (03) ◽  
pp. 773-778 ◽  
Author(s):  
KWOK YEUNG TSANG ◽  
IRA B. SCHWARTZ
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Lyapunov Exponents ◽  
Nonlinear Oscillator ◽  
Nonlinear Oscillators ◽  
Random Time ◽  
High Dimensional ◽  
Coupled Nonlinear Oscillators ◽  
New Type

We discovered the existence of a new type of high-dimensional attractor in coupled nonlinear oscillator systems. Due to the presence of neutrally stable directions on the attractor, there can be noise-driven phase space diffusion. Recurring anti-phase states are observed as coherent portions of the time series. The observed time series looks coherent for a while, then incoherent, and then coherent again. Although the time series “looks” chaotic, the Lyapunov exponents are not positive.

Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group

2018 ◽  
Vol 57 ◽  
pp. 47-57 ◽  
Author(s):  
Ayan Dutta ◽  
Debapriya Das ◽  
Dhruba Banerjee ◽  
Jayanta K. Bhattacharjee
Keyword(s):  
Dynamical System ◽  
Renormalization Group ◽  
Limit Cycle

scholarly journals Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

1997 ◽  
Vol 12 (19) ◽  
pp. 3307-3334 ◽  
Author(s):  
C. Arvanitis ◽  
F. Geniet ◽  
M. Iacomi ◽  
J.-L. Kneur ◽  
A. Neveu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
General Framework ◽  
Free Field ◽  
Variational Calculation ◽  
Final Point ◽  
Variational Calculations ◽  
Perturbative Renormalization ◽  
Good Agreement ◽  
Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

scholarly journals Multi-Critical Multi-Field Models: A CFT Approach to the Leading Order

Universe ◽  
2019 ◽  
Vol 5 (6) ◽  
pp. 151 ◽  
Author(s):  
Gian Paolo Vacca ◽  
Alessandro Codello ◽  
Mahmoud Safari ◽  
Omar Zanusso
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Conformal Field Theory ◽  
Leading Order ◽  
Full Agreement ◽  
Approximate Symmetries ◽  
Conformal Field ◽  
Perturbative Renormalization

We present some general results for the multi-critical multi-field models in d > 2 recently obtained using conformal field theory (CFT) and Schwinger–Dyson methods at the perturbative level without assuming any symmetry. Results in the leading non trivial order are derived consistently for several conformal data in full agreement with functional perturbative renormalization group (RG) methods. Mechanisms like emergent (possibly approximate) symmetries can be naturally investigated in this framework.

The non-perturbative renormalization group

2019 ◽  
pp. 137-144
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Renormalization Group ◽  
Effective Field Theories ◽  
Asymptotic Form ◽  
Effective Field ◽  
Field Theories ◽  
Perturbative Renormalization

Chapter 9 focuses on the non–perturbative renormalization group. Many renormalization group (RG) results are derived within the framework of the perturbative RG. However, this RG is the asymptotic form in some neighbourhood of a Gaussian fixed point of the more general and exact RG, as introduced by Wilson and Wegner, and valid for rather general effective field theories. Chapter 9 describes the corresponding functional RG equations and give some indications about their derivation. A basic role is played by a method of partial field integration, which preserves the locality of the field theory. Note that functional RG equations can also be used to give alternative proofs of perturbative renormalizability within the framework of effective field theories.

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