Absolute Stability of Wavetrains Can Explain Spatiotemporal Dynamics in Reaction-Diffusion Systems of Lambda-Omega Type
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[1] Jonathan A. Sherratt,et al. Oscillations and chaos behind predator–prey invasion: mathematical artifact or ecological reality? , 1997 .
[2] L. Brevdo. Convectively Unstable Wave Packets in the Blasius Boundary Layer , 1995 .
[3] W. Saarloos. Front propagation into unstable states , 2003, cond-mat/0308540.
[4] N. Marcuvitz,et al. Electron-stream interaction with plasmas , 1965 .
[5] M A Lewis,et al. Ecological chaos in the wake of invasion. , 1995, Proceedings of the National Academy of Sciences of the United States of America.
[6] T. Bridges,et al. Absolute and convective instabilities of temporally oscillating flows , 1997 .
[7] Marcus R. Garvie,et al. Numerische Mathematik Finite element approximation of spatially extended predator – prey interactions with the Holling type II functional response , 2007 .
[8] Sergey A. Suslov,et al. Numerical aspects of searching convective/absolute instability transition , 2006, J. Comput. Phys..
[9] Sergei Petrovskii,et al. Dynamical stabilization of an unstable equilibrium in chemical and biological systems , 2002 .
[10] Marcus R. Garvie. Finite-Difference Schemes for Reaction–Diffusion Equations Modeling Predator–Prey Interactions in MATLAB , 2007, Bulletin of mathematical biology.
[11] Paul Wheeler,et al. Computation of Spiral Spectra , 2005, SIAM J. Appl. Dyn. Syst..
[12] S. Suslov. Searching convective/absolute instability boundary for flows with fully numerical dispersion relation , 2001 .
[13] Nancy Kopell,et al. Plane Wave Solutions to Reaction‐Diffusion Equations , 1973 .
[14] J. Sherratt,et al. Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion , 2009, Proceedings of the National Academy of Sciences.
[15] Scheel,et al. Absolute versus convective instability of spiral waves , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[16] Björn Sandstede,et al. Absolute and Convective Instabilities of Waves on Unbounded and Large Bounded Domains , 2022 .
[17] J. Sherratt,et al. Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models , 2008, Journal of The Royal Society Interface.
[18] S. Suslov. Convective and absolute instabilities in non-Boussinesq mixed convection , 2007 .
[19] Irving R Epstein,et al. Localized patterns in reaction-diffusion systems. , 2007, Chaos.
[20] S. Petrovskii,et al. Spatiotemporal patterns in ecology and epidemiology : theory, models, and simulation , 2007 .
[21] A reaction-diffusion system of $\lambda$–$\omega$ type Part II: Numerical analysis , 2005, European Journal of Applied Mathematics.
[22] Jonathan A. Sherratt. On the Evolution of Periodic Plane Waves in Reaction-Diffusion Systems of Lambda-Omega Type , 1994, SIAM J. Appl. Math..
[23] H. Engel,et al. From trigger to phase waves and back again , 2006 .
[24] Björn Sandstede,et al. Gluing unstable fronts and backs together can produce stable pulses , 2000 .
[25] P. Monkewitz,et al. LOCAL AND GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS , 1990 .
[26] P. C. Hohenberg,et al. Fronts, pulses, sources and sinks in generalized complex Ginzberg-Landau equations , 1992 .
[27] Thomas J. Bridges,et al. Absolute and convective instabilities of spatially periodic flows , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[28] L. Brevdo. A study of absolute and convective instabilities with an application to the Eady model , 1988 .
[29] T. Bridges,et al. Linear pulse structure and signalling in a film flow on an inclined plane , 1999, Journal of Fluid Mechanics.
[30] K. Nozaki,et al. Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation , 1985 .
[31] Sergei Petrovskii,et al. Critical phenomena in plankton communities: KISS model revisited , 2000 .
[32] Willy Govaerts,et al. Numerical Continuation of Branch Points of Equilibria and Periodic orbits , 2005, Int. J. Bifurc. Chaos.
[33] M. Cross,et al. Pattern formation outside of equilibrium , 1993 .
[34] S. Paolucci,et al. Stability of non-Boussinesq convection via the complex Ginzburg–Landau model , 2004 .
[35] Nicola J Armstrong,et al. The effects of obstacle size on periodic travelling waves in oscillatory reaction–diffusion equations , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[36] Björn Sandstede,et al. Defects in Oscillatory Media: Toward a Classification , 2004, SIAM J. Appl. Dyn. Syst..
[37] Kazuhiro Nozaki,et al. Exact Solutions of the Generalized Ginzburg-Landau Equation , 1984 .
[38] Björn Sandstede,et al. Computing absolute and essential spectra using continuation , 2007 .
[39] Martin van Hecke. Coherent and Incoherent structures in systems described by the 1D CGLE: Experiments and Identification , 2001 .
[40] I. Aranson,et al. The world of the complex Ginzburg-Landau equation , 2001, cond-mat/0106115.
[41] A. Siamj.. PERIODIC TRAVELLING WAVE SELECTION BY DIRICHLET BOUNDARY CONDITIONS IN OSCILLATORY REACTION-DIFFUSION SYSTEMS∗ , 2003 .
[42] N. Shigesada,et al. Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species , 2001 .
[43] Bifurcation analysis of reaction-diffusion equations—III. Chemical oscillations , 1976 .
[44] J. Chomaz,et al. GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS: Non-Normality and Nonlinearity , 2005 .
[45] A reaction-diffusion system of $\lambda$–$\omega$ type Part I: Mathematical analysis , 2005, European Journal of Applied Mathematics.
[46] Jens D. M. Rademacher,et al. Geometric Relations of Absolute and Essential Spectra of Wave Trains , 2006, SIAM J. Appl. Dyn. Syst..
[47] Shunsaku Nii,et al. The accumulation of eigenvalues in a stability problem , 2000 .
[48] J. Sherratt. The amplitude of periodic plane waves depends on initial conditions in a variety of lambda - omega systems , 1993 .
[49] O. Bjørnstad,et al. Spatial population dynamics: analyzing patterns and processes of population synchrony. , 1999, Trends in ecology & evolution.
[50] B. Sandstede,et al. Chapter 18 - Stability of Travelling Waves , 2002 .
[51] G. Bard Ermentrout,et al. Transition fronts and localized structures in bistable reaction-diffusion equations , 1997 .
[52] Weber,et al. Stability limits of spirals and traveling waves in nonequilibrium media. , 1992, Physical review. A, Atomic, molecular, and optical physics.
[53] E. J. Doedel,et al. AUTO: a program for the automatic bifurcation analysis of autonomous systems , 1980 .
[54] Stability of neuronal pulses composed of concatenated unstable kinks. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.
[55] Grégoire Nicolis,et al. Bifurcation analysis of reaction-diffusion equations—III. Chemical oscillations , 1976 .