125 research outputs found
Standing Waves in the FitzHugh-Nagumo System and a Problem in Combinatorial Geometry
No full textWe show that there is a close relation between standing-wave solutions for the FitzHugh-Nagumo system
\Delta u +u(u-a)(1-u) - \delta v=0, \ \ \Delta v-\delta \gamma v + u=0 \ \ \mbox{in} \ R^N,
u, v \to 0 \ \mbox{as} \ |x| \to +\infty
where and , and the following combinatorial problem:
{\it Given points with minimum distance , find out the maximum number of times that the minimum distance can occur. }
More precisely, we show that for any given positive integer , there exists a such that for , there exists a standing-wave solution to the FitzHugh-Nagumo system with the property that has spikes and approaches an optimal configuration in (*), where
Stochastic FitzHugh-Nagumo Equations
No full textThe stochastic FitzHugh-Nagumo equations are a system of stochastic partial differential equations that describes the propagation of action potentials along nerve axons. In the present work we obtain well-posedness and regularisation results for the FitzHugh-Nagumo equations with domain R^d. We begin by considering the weak critical variational setting, where we prove global well-posedness for the case d=1. We subsequently consider the strong variational setting, which allows us to extend our well-posedness results to d <= 4. To prove well-posedness and regularisation for arbitrary d, we consider the FitzHugh-Nagumo equations in the L^p(L^q)-setting. Building on earlier results for reaction-diffusion equations, we first prove well-posedness on the d-dimensional flat torus and use bootstrapping techniques to prove instantaneous regularisation of the solution. We subsequently extend the theory for reaction-diffusion equations to the unbounded domain R^d to finally prove well-posedness and regularisation for the FitzHugh-Nagumo equations on R^d.Applied Mathematic
Finding Aid for the Bill Fitzhugh Collection (MUM00786)
No full textThis collection contains the research, notes, publications, photographs, and drafts of author Bill Fitzhugh
Sometimes you have to lie the life and times of Louise Fitzhugh, renegade author of Harriet the spy
No full textLouise Fitzhugh's books are full of resistance: to liars, to conformity, to authority, and even (radically, for a children's author) to make-believe. As a commercial children's author and lesbian, Fitzhugh often had to disguise the nature of her most intimate relationships. She lived her life as a dissenter--a friend to underdogs, outsiders, and artists--and her masterpiece remains long after her death to influence and provoke new generations of readers. Harriet is massively influential among girls and women in contemporary culture; she is the missing link between Jo March and Scout Finch, and it's not surprising that writers have thought of her as a kind of patron saint for misfit writers and unfeminine girls. This biography brings Harriet's creator into the frame, shedding new light on the author and her work"The protagonist and anti-heroine of Louise Fitzhugh's masterpiece Harriet the Spy, first published first in 1964, continues to mesmerize generation after generation of readers. Harriet is an erratic, unsentimental, and endearing prototype--someone very like the woman who dreamed her up, author and artist Louise Fitzhugh. Born in 1928, Fitzhugh was raised in a wealthy home in segregated Memphis, and she escaped her cloistered world and made a beeline for New York as soon as she could. Her expanded milieu stretched from the lesbian bars of Greenwich Village to the dance clubs of Harlem, on to the resurgent artist studios of post-war New York, France, and Italy. Her circle of friends included artists like Maurice Sendak and playwrights like Lorraine Hansberry. In the 1960s, Fitzhugh wrote Harriet the Spy, and in doing so she introduced "new realism" into children's books--she launched a genre of children's books that allowed characters to experience authentic feelings and acknowledged topics that were formerly considered taboo. Fitzhugh's books are full of resistance: to liars, to conformity, to authority, and even (radically, for a children's author) to make-believe. As a commercial children's author and lesbian, Fitzhugh often had to disguise the nature of her most intimate relationships. She lived her life as a dissenter--a friend to underdogs, outsiders, and artists--and her masterpiece remains long after her death to influence and provoke new generations of readers. Harriet is massively influential among girls and women in contemporary culture; she is the missing link between Jo March and Scout Finch, and it's not surprising that writers have thought of her as a kind of patron saint for misfit writers and unfeminine girls. This lively, rich biography brings Harriet's creator into the frame, shedding new light on an extraordinary author and her marvelous creation"-
Periodic solutions of a periodic FitzHugh-Nagumo differential system
No full textAgraïments: The second author is partially supported by Dirección de Investigación DIUBB 1204084/R.Recently some interest has appeared for the periodic FitzHugh-Nagumo differential systems. Here, we provide sufficient conditions for the existence of periodic solutions in such differential systems
Periodic solutions of a periodic FitzHugh-Nagumo differential system
No full textAgraïments: The second author is partially supported by Dirección de Investigación DIUBB 1204084/R.Recently some interest has appeared for the periodic FitzHugh-Nagumo differential systems. Here, we provide sufficient conditions for the existence of periodic solutions in such differential systems
Zero-Hopf bifurcation in the Fitzhugh-Nagumo system
No full textAgraïments: The first author is supported by the FAPESP-BRAZIL grants 2010/18015-6 and 2012/05635-1. The third author is partially supported by Dirección de Investigación DIUBB 120408 4/R.We characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+ and P− in the FitzHugh-Nagumo system. Thus we find two 2-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at the origin is a zero-Hopf equilibrium. For these two families we prove the existence of a periodic orbit bifurcating from the zero-Hopf equilibrium point O. We prove that exist three 2-parameter families of the FitzHughNagumo system for which the equilibrium point at P+ and P− is a zero-Hopf equilibrium point. For one of these families we prove the existence of 1, or 2, or 3 periodic orbits borning at P+ and P−
Zero-Hopf bifurcation in the Fitzhugh-Nagumo system
No full textAgraïments: The first author is supported by the FAPESP-BRAZIL grants 2010/18015-6 and 2012/05635-1. The third author is partially supported by Dirección de Investigación DIUBB 120408 4/R.We characterize the values of the parameters for which a zero-Hopf equilibrium point takes place at the singular points, namely, O (the origin), P+ and P- in the FitzHugh-Nagumo system. Thus we find two 2-parameter families of the FitzHugh-Nagumo system for which the equilibrium point at the origin is a zero-Hopf equilibrium. For these two families we prove the existence of a periodic orbit bifurcating from the zero-Hopf equilibrium point O. We prove that exist three 2-parameter families of the FitzHughNagumo system for which the equilibrium point at P+ and P- is a zero-Hopf equilibrium point. For one of these families we prove the existence of 1, or 2, or 3 periodic orbits borning at P+ and P-
Genealogy of the Fitzhugh, Knox, Gordon, Selden, Horner, Brown, Baylor, (King) Carter, Edmonds, Digges, Page, Tayloe and allied families;
No full textTraces the descent of the author through each family."This is a limited edition of 1000 copies." No.119.Title from cover.Mode of access: Internet
Further results on approximate inertial manifolds for the FitzHugh-Nagumo model
No full textFor two particular choices of the three parameters in the FitzHugh-Nagumo model the equilibrium points are found. The corresponding phase portrait around them is graphically represented allowing us to delimit an absorbing domain. Then the Jolly-Rosa-Temam numerical method is applied in order to study the approximate inertial manifold for the model. To this aim the own numerical code of the first author is used
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