Generic Hopf Bifurcation From Lines of Equilibria Without Parameters: II. Systems of Viscous Hyperbolic Balance Laws
نویسندگان
چکیده
We investigate viscous shock profiles of the Riemann problem for systems of hyperbolic balance laws. Even strictly hyperbolic flux terms together with a nonoscillating kinetic part can lead to oscillating viscous shock profiles. They appear near a Hopf-like bifurcation point of the traveling wave equation.
منابع مشابه
Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory
Motivated by decoupling e ects in coupled oscillators, by viscous shock proles in systems of nonlinear hyperbolic balance laws, and by binary oscillation e ects in discretizations of systems of hyperbolic balance laws, we consider vector elds with a one-dimensional line of equilibria, even in the absence of any parameters. Besides a trivial eigenvalue zero we assume that the linearization at th...
متن کاملGeneric Hopf bifurcation from Lines of Equilibria without parameters III: Binary oscillations
We consider discretized systems of hyperbolic balance laws. Decoupling of the flow, associated to a central difference scheme, can lead to binary oscillations — even and odd numbered grid points, separately, provide time-evolutions of two distinct, different, separate profiles. Investigating the stability of this decoupling phenomenon, we encounter Hopflike bifurcations in the absence of parame...
متن کاملStable, Oscillatory Viscous Profiles of Weak Shocks in Systems of Stiff Balance Laws
This paper is devoted to a phenomenon in hyperbolic balance laws, first described by Fiedler and Liebscher [2], which is similar in spirit to the Turing instability. The combination of two individually stabilising effects can lead to quite rich dynamical behaviour, like instabilities, oscillations, or pattern formation. Our problem is composed of two ingredients. First, we have a strictly hyper...
متن کاملNormal forms of Hopf Singularities: Focus Values Along with some Applications in Physics
This paper aims to introduce the original ideas of normal form theory and bifurcation analysis and control of small amplitude limit cycles in a non-technical terms so that it would be comprehensible to wide ranges of Persian speaking engineers and physicists. The history of normal form goes back to more than one hundreds ago, that is to the original ideas coming from Henry Poincare. This tool p...
متن کاملThreshold harvesting policy and delayed ratio-dependent functional response predator-prey model
This paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. We study the equilibria of the system before and after the threshold. We show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. The global analysis of the model as well as boundedness and permanence properties a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 31 شماره
صفحات -
تاریخ انتشار 2000