5 edition of **Hopf bifurcation in the two locus genetic model** found in the catalog.

- 92 Want to read
- 9 Currently reading

Published
**1983**
by American Mathematical Society in Providence, R.I
.

Written in English

- Genetics -- Mathematical models.,
- Bifurcation theory.

**Edition Notes**

Statement | Ethan Akin. |

Series | Memoirs of the American Mathematical Society,, no. 284 (July 1983), Memoirs of the American Mathematical Society ;, no. 284. |

Classifications | |
---|---|

LC Classifications | QA3 .A57 no. 284, QH438.4.M3 .A57 no. 284 |

The Physical Object | |

Pagination | v, 190 p. ; |

Number of Pages | 190 |

ID Numbers | |

Open Library | OL3164522M |

ISBN 10 | 0821822845 |

LC Control Number | 83006438 |

HOPF BIFURCATION AND TURING INSTABILITY For a given point (x0,y0) ∈ D2, denote T1 as the time of the trajectory running from (x0,y0) to C1and T2(N) as the time of the trajectory running from (x0,y0) to the line x = x0/N, N ∈ N and N 2. We estimate the time T1 and T2. T1 1 y0 1 sy 1 − y x dy y 0 1 1 sy y 0 −1 dy = 1 s ln 1 − x0 y0 1 −x0 It is clear that T1 is ﬁnite. While. HOPF BIFURCATIONS AND LIMIT CYCLES IN EVOLUTIONARY NETWORK DYNAMICS DARREN PAIS y, CARLOS H. CAICEDO-NU NEZ~ y, AND NAOMI E. LEONARD Abstract. The replicator-mutator equations from evolutionary dynamics serve as a model for the evolution of language, behavioral dynamics in social networks, and decision-making dynamics in .

Hopf bifurcation is a critical point where a system’s stability switches and a periodic solution arises local bifurcation in which a xed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues (of the linearization around the xed point) cross the complex plane imaginary axis. Angela Peace 6/14File Size: KB. Discover Book Depository's huge selection of Ethan Akin books online. Free delivery worldwide on over 20 million titles.

Bifurcation analysis of chemical reaction mechanisms. II. Hopf bifurcation analysis ric signature, the codimension two Hopf bifurcation lead- ing ‘ to multiple periodic orbits does not. Identification of the latter type Hopf bifurcation is important because it is often responsible for the frequently observed situation in. Book Description The `Hopf Bifurcation' describes a phenomenon that occurs widely in nature: the birth of a family of oscillations as a controlling parameter is varied. In a control system consisting of an engine with a centrifugal governor, for example, when the amount of damping associated with the governor is decreased, oscillations can Author: B. D. Hassard, N. D. Kazarinoff, Y.-H. Wan.

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This will be a useful book for readers of a topological bent already familiar with the basics of dynamical systems theory; it contains much fundamental material, tells a unified story, and has appeared at the right time. Hopf Bifurcation in the Two Locus Genetic Model Base Product Code Keyword List: memo; MEMO; Hopf Bifurcation in the.

Get this from a library. Hopf bifurcation in the two locus genetic model. [Ethan Akin] -- Hopf bifurcations occur in the class of simple genetic models for the combined effect of selection and recombination.

The demonstration of cycling in such models is. Genre/Form: Electronic books: Additional Physical Format: Print version: Akin, Ethan, Hopf bifurcation in the two locus genetic model / Material Type. In the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where a system's stability switches and a periodic solution arises.

More accurately, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues - of the linearization around the fixed point - crosses the complex plane imaginary axis. This Demonstration allows interactive manipulation of the Sel'kov model for glycolysis—an important metabolic pathway in which glucose is broken down to make pyruvate.

The model exhibits a Hopf bifurcation as the key parameter is varied. Hopf bifurcations occur in the class of simple genetic models for the combined effect of selection and recombination. The demonstration of cycling in such models is biologically unexpected.

To study this phenomenon we describe the locus of positions at which Hopf bifurcation occurs in the two-locus-two-allele model. Biological applications of bifurcation theory provide a framework for understanding the behavior of biological networks modeled as dynamical the context of a biological system, bifurcation theory describes how small changes in an input parameter can cause a bifurcation or qualitative change in the behavior of the system.

The ability to make dramatic change in. [1] and their co-workers starting around Hopf's basic paper [1] appeared in Although the term "Poincare Andronov-Hopf bifurcation" is more accurate (sometimes Friedrichs is also included), the name "Hopf Bifurcation" seems more common, so we have used it.

Hopf's crucial contribution was the extension from two dimensions to higher. Hopf bifurcation analysis for genetic regulatory networks with two delays Smolen et al.

proposed a model in the form of two ordinary. some. Therefore, the two intersections of R e (λ 1) curve and lateral axis are Hopf Bifurcation points of the model.

The values of the first intersection are V = – mV, I = μA/cm 2. The key parameter β w has a crucial impact on Hopf bifurcation of the model. Hopf bifurcation points change when β w has different by: 1. In this paper, we deal with a model of single genetic negative feedback autoregulatory system with delay.

Choosing the transcriptional rate k as the bifurcation parameter, we demonstrate that the Hopf bifurcation would occur when k exceeds a critical value. By using the normal form theory and center manifold argument, we derive the explicit formulas which determine the bifurcation Cited by: Andronov-Hopf bifurcation (ﬁrst described by Hopf [27]), a steady state changes stability as two complex conjugate eigenvalues of the linearization cross the imaginary axis and a family of periodic orbits bifurcates from the steady state.

Many. As you can see in the snapshots, there are two Hopf bifurcation points. Indeed, for, the steady state is a stable focus; for, the trajectory is attracted to a stable periodic solution (called a limit cycle); and finally for, the steady state is again a stable focus.

For, the two Hopf bifurcation points are obtained at and. The mathematics is not very deep but it is unfamiliar to many, so we begin with a survey of the elements of linear algebra on Euclidean vector spaces and of calculus on Riemannian manifolds.

We then apply the Shahshahani metric to population genetics, deriving the occurrence of cycling in the two locus, two allele by: Then we present sufficient conditions for the local stability of two-gene genetic regulatory networks in the parameter space, and assess critical values of the Hopf bifurcation.

System can be used not only to indicate the occurrence of oscillations, but also to detect the robustness of amplitudes against variation in delays. The bifurcation diagram of system for protein p is shown in Fig. 5, where the control parameter is the total time delay low values of τ, the system reaches a stable steady state corresponding to some constant concentrations of the Cited by: Hopf Bifurcation in the Two Locus Genetic Model (Memoirs of the American Mathematical Society) Jul 1, by Ethan Akin Paperback.

() Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays. Advances in Applied Mathematics and Mechanics() Delay-induced oscillatory dynamics in humoral mediated immune response with two time by: Hopf Bifurcation Double Heterozygote Selection Matrix Unique Positive Root Discrete Time Analogue These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm by: 9. Theory And Application Of Hopf Bifurcation book. Read reviews from world’s largest community for readers.

The Hopf Bifurcation' describes a phenomenon th /5. ing model dθi dt = ωi+ K N XN j=1 sin(θj− θi)+hsin2(θj− θi), () will be considered, where his a parameter which controls the strength of the second harmonic. For the continuous limit of the system, a Hopf bifurcation from the incoherent state to the two-cluster periodic state will be investigated based on the generalized spectral.This paper is concerned with a computer virus model with two delays.

Its dynamics are studied in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the positive equilibrium and existence of the local Hopf bifurcation are obtained by regarding the possible combinations of the two delays as a bifurcation by: 6.We research the dynamics of the chemostat model with time delay.

The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. By using the normal form theory and center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic by: 3.