Advanced Topics: Instability Hierarchies of Self-Organization Systems and Devices

[1]  L. Wolpert Positional information and the spatial pattern of cellular differentiation. , 1969, Journal of theoretical biology.

[2]  J. Murray A Pre-pattern formation mechanism for animal coat markings , 1981 .

[3]  K. Tomita,et al.  Chaotic response of nonlinear oscillators , 1982 .

[4]  Ki-ichi Nakamura Statistical Dynamics of the Gunn Instability near Threshold , 1975 .

[5]  P. Morse,et al.  Methods of theoretical physics , 1955 .

[6]  J. B. Gunn,et al.  Instabilities of Current in III-V Semiconductors , 1964, IBM J. Res. Dev..

[7]  G. Pfister,et al.  Space-dependent order parameter in circular couette flow transitions , 1981 .

[8]  H. Haken,et al.  The influence of noise on the logistic model , 1981 .

[9]  J. D. Farmer,et al.  Chaotic attractors of an infinite-dimensional dynamical system , 1982 .

[10]  A. J. Lotka Analytical Note on Certain Rhythmic Relations in Organic Systems , 1920, Proceedings of the National Academy of Sciences.

[11]  Marlan O. Scully,et al.  Quantum Theory of an Optical Maser. 1. General Theory , 1967 .

[12]  R. Graham Solution of Fokker Planck equations with and without manifest detailed balance , 1980 .

[13]  Elliott W. Montroll,et al.  Nonlinear Population Dynamics. (Book Reviews: On the Volterra and Other Nonlinear Models of Interacting Populations) , 1971 .

[14]  P. Bergé,et al.  Experiments on hydrodynamic instabilities and the transition to turbulence , 1979 .

[15]  C. Krebs Ecology: The Experimental Analysis of Distribution and Abundance , 1973 .

[16]  J. Gunn Microwave oscillations of current in III–V semiconductors , 1993 .

[17]  Goal: Why You Might Read This Book , 1977 .

[18]  J. Gollub,et al.  Many routes to turbulent convection , 1980, Journal of Fluid Mechanics.

[19]  C. Zener A theory of the electrical breakdown of solid dielectrics , 1934 .

[20]  Hermann Haken,et al.  Quantum theory of light propagation in a fluctuating laser-active medium , 1968 .

[21]  Chih-fen Chang,et al.  Qualitative Theory of Differential Equations , 1992 .

[22]  F. Busse,et al.  On the stability of steady finite amplitude convection , 1965, Journal of Fluid Mechanics.

[23]  Friedrich H. Busse,et al.  The stability of finite amplitude cellular convection and its relation to an extremum principle , 1967, Journal of Fluid Mechanics.

[24]  D. Ter Haar,et al.  Langmuir turbulence and modulational instability , 1978 .

[25]  Alan S. Perelson,et al.  Chemical reaction dynamics part II: Reaction networks , 1974 .

[26]  L. Mockros,et al.  The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations , 1972, Journal of Fluid Mechanics.

[27]  G. Ahlers,et al.  Turbulence near Onset of Convection , 1980 .

[28]  Shang‐keng Ma Modern Theory of Critical Phenomena , 1976 .

[29]  V. I. Arnol'd,et al.  PROOF OF A THEOREM OF A.?N.?KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN , 1963 .

[30]  H. Haken,et al.  Some exact results on discrete noisy maps , 1982 .

[31]  L. Esaki New Phenomenon in Narrow Germanium p-n Junctions , 1958 .

[32]  S. Stenholm,et al.  Gas Laser with Saturable Absorber. I. Single-Mode Characteristics , 1973 .

[33]  A. Chenciner,et al.  Bifurcations de tores invariants , 1979 .

[34]  Harald Bergstriim Mathematical Theory of Probability and Statistics , 1966 .

[35]  A. Zhabotinsky,et al.  Autowave processes in a distributed chemical system. , 1973, Journal of theoretical biology.

[36]  F. Cap Handbook on plasma instabilities , 1976 .

[37]  F. Takens,et al.  Occurrence of strange AxiomA attractors near quasi periodic flows onTm,m≧3 , 1978 .

[38]  G. Caglioti,et al.  Gruneisen parameter: measurement of the strain derivatives , 1981 .

[39]  E. Coddington,et al.  Theory of Ordinary Differential Equations , 1955 .

[40]  Louis A. P. Balázs Planar bootstrap based on a Pade approximation to the dual multiperipheral model , 1977 .

[41]  F. Busse,et al.  Non-linear properties of thermal convection , 1978 .

[42]  H. Haken,et al.  Analytical treatment of pattern formation in the Gierer-Meinhardt model of morphogenesis , 1978 .

[43]  M. Giglio,et al.  Transition to Chaotic Behavior via a Reproducible Sequence of Period-Doubling Bifurcations , 1981 .

[44]  C. Eugene Wayne,et al.  Scaling Theory for Noisy Period-Doubling Transitions to Chaos , 1981 .

[45]  Y. Pomeau,et al.  Intermittent transition to turbulence in dissipative dynamical systems , 1980 .

[46]  Hermann Haken,et al.  Laserlight — first example of a second-order phase transition far away from thermal equilibrium , 1970 .

[47]  Hermann Haken,et al.  Synergetik — die Lehre vom Zusammenwirken , 1989 .

[48]  Jürgen Moser,et al.  Convergent series expansions for quasi-periodic motions , 1967 .

[49]  E. Koschmieder,et al.  Heat transfer through a shallow, horizontal convecting fluid layer , 1974 .

[50]  G. Oster,et al.  Chemical reaction dynamics , 1974 .

[51]  Rolf Landauer,et al.  Cooperative Phenomena in Data Processing , 1973 .

[52]  C. Gardiner Handbook of Stochastic Methods , 1983 .

[53]  Hermann Haken,et al.  Generalized Ginzburg-Landau equations, slaving principle and center manifold theorem , 1981 .

[54]  S. Mccall Instabilities in continuous-wave light propagation in absorbing media , 1974 .

[55]  Y. Pesin CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY , 1977 .

[56]  Giles W Hunt,et al.  A general theory of elastic stability , 1973 .

[57]  Lee A. Segel,et al.  Non-linear wave-number interaction in near-critical two-dimensional flows , 1971, Journal of Fluid Mechanics.

[58]  Hermann Haken,et al.  Dynamics of Synergetic Systems , 1980 .

[59]  H. Meinhardt,et al.  A theory of biological pattern formation , 1972, Kybernetik.

[60]  H. Haken Selforganization through Increase of Number of Components , 1980 .

[61]  G. Taylor Stability of a Viscous Liquid Contained between Two Rotating Cylinders , 1923 .

[62]  R. Behringer,et al.  Evolution of Turbulence from the Rayleigh-Bénard Instability , 1978 .

[63]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[64]  R. M. Noyes,et al.  Oscillatory Chemical Reactions , 1974 .

[65]  H. Haken,et al.  Chapman-Kolmogorov equation and path integrals for discrete chaos in presence of noise , 1981 .

[66]  H. Haken,et al.  Generalized thermodynamic potential for Markoff systems in detailed balance and far from thermal equilibrium , 1971 .

[67]  K. Wilson Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior , 1971 .

[68]  Hermann Haken,et al.  At least one Lyapunov exponent vanishes if the trajectory of an attractor does not contain a fixed point , 1983 .

[69]  René Thom,et al.  Structural stability and morphogenesis , 1977, Pattern Recognit..

[70]  Luigi A. Lugiato,et al.  Optical bistability, instabilities and higher order bifurcations , 1981 .

[71]  R. L. Stratonovich A New Representation for Stochastic Integrals and Equations , 1966 .

[72]  J. Hutchinson,et al.  Buckling of Bars, Plates and Shells , 1975 .

[73]  H. Haken Exact stationary solution of a Fokker-Planck equation for multimode laser action including phase locking , 1969 .

[74]  F. Busse,et al.  An asymptotic model of two-dimensional convection in the limit of low Prandtl number , 1981, Journal of Fluid Mechanics.

[75]  C. Chiu,et al.  STATISTICAL BOOTSTRAP MODEL OF HADRONS WITH SPIN. , 1971 .

[76]  L. Lugiato,et al.  Cooperative effects and bistability for resonance fluorescence , 1976 .

[77]  G. Iooss Bifurcation of maps and applications , 1979 .

[78]  M. Eigen Selforganization of matter and the evolution of biological macromolecules , 1971, Naturwissenschaften.

[79]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[80]  James P. Crutchfield,et al.  Fluctuations and the onset of chaos , 1980 .

[81]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[82]  Robert Graham,et al.  Hydrodynamic fluctuations near the convection instability , 1974 .

[83]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion , 1930 .

[84]  H. D. Vollmer,et al.  The transient solution of the laser Fokker-Planck equation , 1967 .

[85]  F. Busse The oscillatory instability of convection rolls in a low Prandtl number fluid , 1972, Journal of Fluid Mechanics.

[86]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[87]  J. Langer Instabilities and pattern formation in crystal growth , 1980 .

[88]  D'arcy W. Thompson On growth and form i , 1943 .

[89]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[90]  Donald Ludwig Stochastic Population Theories , 2011 .

[91]  Lord Rayleigh,et al.  LIX. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side , 1916 .

[92]  H. Haken,et al.  Intermittent behavior of the logistic system , 1981 .

[93]  Charles DeLisi,et al.  Antigen Antibody Interactions , 1976 .

[94]  Yoshiki Kuramoto,et al.  Reductive Perturbation Approach to Chemical Instabilities , 1974 .

[95]  M. Eigen,et al.  The Hypercycle , 2004, Naturwissenschaften.

[96]  H. Swinney,et al.  Dynamical instabilities and the transition to chaotic Taylor vortex flow , 1979, Journal of Fluid Mechanics.

[97]  James P. Crutchfield,et al.  Scaling for External Noise at the Onset of Chaos , 1981 .

[98]  Hermann Haken,et al.  Slaving principle for stochastic differential equations with additive and multiplicative noise and for discrete noisy maps , 1982 .

[99]  F. Wegner Critical Exponents in Isotropic Spin Systems , 1972 .

[100]  E. Schmidt,et al.  Zur Theorie der linearen und nichtlinearen Integralgleichungen. III. Teil , 1908 .

[101]  R. Graham Generalized Thermodynamic Potential for the Convection Instability , 1973 .

[102]  H Shimizu Dynamic cooperativity of molecular processes in active streaming, muscle contraction, and subcellular dynamics: the molecular mechanism of self-organization at the subcellular level. , 1979, Advances in biophysics.

[103]  Kiyosi Itô Stochastic Differential Equations in a Differentiable Manifold , 1950, Nagoya Mathematical Journal.

[104]  W. C. Bray A PERIODIC REACTION IN HOMOGENEOUS SOLUTION AND ITS RELATION TO CATALYSIS. , 1921 .

[105]  F. Takens,et al.  On the nature of turbulence , 1971 .

[106]  H. Haken Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems , 1975 .

[107]  Hermann Haken,et al.  Chaos and Order in Nature , 1981 .

[108]  P. Linsay Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator , 1981 .

[109]  G. Sell,et al.  The Hopf Bifurcation and Its Applications , 1976 .

[110]  H. Risken Distribution- and correlation-functions for a laser amplitude , 1965 .

[111]  H. Haken,et al.  Pattern formation in morphogenesis , 1982, Journal of mathematical biology.

[112]  J. Swift,et al.  Hydrodynamic fluctuations at the convective instability , 1977 .

[113]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

[114]  G. Floquet,et al.  Sur les équations différentielles linéaires à coefficients périodiques , 1883 .

[115]  Harry L. Swinney,et al.  Hydrodynamic instabilities and the transition to turbulence , 1981 .

[116]  John Whitehead,et al.  Finite bandwidth, finite amplitude convection , 1969, Journal of Fluid Mechanics.

[117]  Kiyosi Itô On a formula concerning stochastic differentials , 1951 .

[118]  H. Risken Solutions of the Fokker-Planck equation in detailed balance , 1972 .

[119]  Hamel Georg Duffing, Ingenieur: Erzwungene Schwingungen bei veränderlicher Eigenfrequenz und ihre technische Bedeutung. Sammlung Vieweg. Heft 41/42, Braunschweig 1918. VI+134 S , 2022 .

[120]  J. Zorell Self-pulsing in ring lasers with detuning , 1981 .

[121]  D. Ruelle SENSITIVE DEPENDENCE ON INITIAL CONDITION AND TURBULENT BEHAVIOR OF DYNAMICAL SYSTEMS , 1979 .

[122]  Werner Ebeling,et al.  Physik der Selbstorganisation und Evolution , 1984 .

[123]  George R. Sell,et al.  Bifurcation of higher dimensional tori , 1979 .

[124]  H. Risken,et al.  Instability of laser cw oscillation in the presence of a passive medium , 1978 .

[125]  R. Landauer Fluctuations in Bistable Tunnel Diode Circuits , 1962 .

[126]  V. Belyaev,et al.  Calculation of low-energy pion—3He scattering , 1979 .

[127]  Paul C. Fife,et al.  Mathematical Aspects of Reacting and Diffusing Systems , 1979 .

[128]  M. Lax,et al.  Classical Noise. VI. Noise in Self-Sustained Oscillators near Threshold , 1967 .

[129]  H. Poincaré,et al.  Les méthodes nouvelles de la mécanique céleste , 1899 .

[130]  N. Bogolyubov,et al.  Asymptotic Methods in the Theory of Nonlinear Oscillations , 1961 .

[131]  H. Haken,et al.  Frequency shifts of laser modes in solid state and gaseous systems , 1963 .