boundary effects on localized structures in spatially extended systems abstract we present a general method of analyzing the influence of finite size and boundary effects on the dynamics of localized solutions of non linear spatially extended systems the dynamics of localized structures in infinite systems involve solvability conditions that require projection onto a goldstone mode our method works by extending the solvability conditions to finite sized systems by incorporating the finite sized modifications of the goldstone mode and associated nonzero eigenvalue we apply this method to the special case of non equilibrium domain walls under the influence of dirichlet boundary conditions in a parametrically forced complex ginzburg landau equation where we examine exotic nonuniform domain wall motion due to the influence of boundary conditions

from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

an implicit non linear time dependent equation has a solution has a solution u u w the operators s l and a t are maximal monotone from a real hilbert space v to its dual such that r 9 r are v coercive and a r are not degenerate a linear compact injection i embeds v to a real banach space w and each d r is the strongly monotone subdifferential of a continuous convex function i on w the function f is square integrable the functions w r v w are lipschitzian as v valued functions section 3 contains the theorems the main result is theorem 2 theorems 3 and 4 demonstrate the smoothing effect on the initial condition their proofs are given in section 4 they exploit the methods of di benedetto and showalter 4 who studied this equation in the case where d and a do not depend on time and v 0 but d can be degenerate grange and mignot studied a similar autonomous equation without v 7 saguez introduced the operator w 111 exploiting their methods by which he later proved together with bermudez and durany the solvability if 9j does not depend on time 131 in section 6 there is an example more examples in the time independent case as remarks and counterexamples on the uniqueness of the solution can be found in 4

global solution to a singular integro differential system related to the entropy balance this paper is devoted to the mathematical analysis of a thermodynamic model describing phase transitions with thermal memory in terms of an entropy equation and a momentum balance for the microforces the initial and boundary value problem is addressed for the related integro differential system of partial differential equations pdes existence and uniqueness continuous dependence on the data and regularity results are proved for the global solution in a finite time interval

an intrinsic characterization of kahler manifolds on etudie la condition de kahler pour une variete complexe compacte on caracterise les varietes complexes compactes qui admettent des metriques de kahler

stability of the bloch wall via the bogomolnyi decomposition in elliptic coordinates we consider the one dimensional anisotropic xy model in the continuum limit stability analysis of its bloch wall solution is hindered by the non diagonality of the associated linearized operator and the hessian of energy we circumvent this difficulty by showing that the energy admits a bogomolnyi bound in elliptic coordinates and that the bloch wall saturates it that is the bloch wall renders the energy minimum our analysis provides a simple but nontrivial application of the bps bogomolnyi prasad sommerfield construction in one dimension where its use is often believed to be limited to reproducing results obtainable by other means

existence for a doubly nonlinear volterra equation abstract we consider a doubly nonlinear volterra equation involving a nonsmooth kernel and two possibly degenerate monotone operators by exploiting an implicit time discretization procedure we obtain the existence of a global strong solution and extend to the nonlocal in time situation some former results by colli p colli on some doubly nonlinear evolution equations in banach spaces japan j indust appl math 9 2 1992 181 203

on the interaction of spiral waves in non equilibrium media abstract we show that the asymptotic interaction of spirals in two dimensionally oscillating continuous media falls off exponentially and can be attractive as well as repulsive depending on the parameters of the system but not on the topological charges the exponent is in qualitative agreement with simulations for moderate distances the simulations show that spirals may form a stable bound state pairs with opposite topological charges drift with constant velocity and like charged spirals rotate around each other with constant frequency this is in contrast with the stationary non oscillating case where the interaction of vortices or dislocations is long range and monotonical and depends on topological charges

perturbation of a hopf bifurcation by an external time periodic forcing contenrs i introduction ii the mathematical model iii dynamics of the poincark map in the non resonant and weakly resonant cases iv dynamics of the poincark map in the p l resonant case v dynamics of the poincart map in the p 2 resonant case vi dynamics of the poincark map in the p 3 resonant case

bifurcations in a stock market model abstract a theoretical framework is laid out where a stock exchange is represented as a process under decentralized control attention is devoted to a specific case in which the trading activity is described by a second order dynamical system three economically significant modes of behavior are identified the stock market can 1 adjust to a stable equilibrium 2 approach a stable limit cycle 3 diverge to infinity the transition from mode 1 to mode 2 is a supercritical hopf bifurcation whereas the transition from mode 2 to mode 3 is a homoclinic bifurcation

pattern formation in the strong resonant forcing of spatially distributed oscillators abstract this paper is devoted to the study of the strongly resonant forcing of the hopf bifurcation in the weak forcing limit pattern formation can be seen as the stabilization of the modulational instability applications to patterns in optics are considered

global bifurcations in rayleigh be nard convection experiments empirical maps and numerical bifurcation analysis abstract we use nonlinear signal processing techniques based on artificial neural networks to construct an empirical mapping from experimental rayleigh benard convection data in the quasiperiodic regime the data in the form of a one parameter sequence of poincare sections in the interior of a mode locked region resonance horn are indicative of a complicated interplay of local and global bifurcations with respect to the experimentally varied rayleigh number the dynamic phenomena apparent in the data include period doublings complex intermittent behavior secondary hopf bifurcations and chaotic dynamics we use the fitted map to reconstruct the experimental dynamics and to explore the associated local and global bifurcation structures in phase space using numerical bifurcation techniques we locate the stable and unstable periodic solutions calculate eigenvalues approximate invariant manifolds of saddle type solutions and identify bifurcation points this approach constitutes a promising data post processing procedure for investigating phase space and parameter space of real experimental systems it allows us to infer phase space structures which the experiments can only probe with limited measurement precision and only at a discrete number of operating parameter settings

harmonic forcing of an extended oscillatory system homogeneous and periodic solutions in this paper we study the effect of external harmonic forcing on a one dimensional oscillatory system described by the complex ginzburg landau equation cgle for a sufficiently large forcing amplitude a homogeneous state with no spatial structure is observed the state becomes unstable to a spatially periodic stripe state via a supercritical bifurcation as the forcing amplitude decreases an approximate phase equation is derived and an analytic solution for the stripe state is obtained through which the asymmetric behavior of the stability border of the state is explained the phase equation in particular the analytic solution is found to be very useful in understanding the stability borders of the homogeneous and stripe states of the forced cgle

discretization with variable time steps of an evolution equation with a positive type memory term we consider the linearized form of an evolution equation used to model viscoelasticity and heat conduction in materials with memory the equation is discretized in time using several schemes based on the backward euler and crank nicolson methods and incorporating appropriate quadratures for the memory term by permitting variable time steps we remove a restriction present in earlier related work by the first two authors

bifurcations with imperfect so 2 symmetry and pinning of rotating waves rotating waves are periodic solutions in so 2 equivariant dynamical systems their precession frequency changes with parameters and it may change sign passing through zero when this happens the

doubly nonlinear equations with unbounded operators abstract the solvability of the evolution system v t b t u t f t v t a t u t 0 a t are bounded possibly degenerate subdifferentials and b t are unbounded subdifferentials

hopf bifurcation analysis of a rotor seal system abstract the hopf bifurcation behaviour of a symmetric rotor seal system was investigated using muszynska s non linear seal fluid dynamic force model for a perfectly balanced system the instability from certain critical equilibrium positions is proved to be the result of hopf bifurcation and only the supercritical type is found for a specific rotor system using poore s algebraic criteria hence a stable periodic orbit bifurcates from the critical equilibrium position after the threshold speed is exceeded due to the dimensionless whirl frequency being found to be close to 1 2 over quite a large range of system parameters the periodically perturbed hopf bifurcation in 1 2 subharmonic resonance is dealt with for an imbalanced rotor system the bifurcation of the averaged system obtained using the centre manifold procedure and averaging method is analyzed the results show that non synchronized whirl of the imbalanced rotor can either be a quasi periodic motion resulting from a hopf bifurcation or a half frequency whirl from period doubling bifurcation determined by the structure parameters of the system and operation conditions numerical simulation verifies the analytical results

mel nikov s function for two dimensional mappings this paper calculates explicitly the mel nikov function for general perturbations of two dimensional maps possessing a saddle connection this result may be considered as the discrete analogue of ziglin s calculation of the mel nikov function for time periodic perturbations of two dimensional continuous flows key words integrable planar maps perturbations homoclinic orbits mel nikov s function poisson summation formula

higher order approximation of subharmonics close to strong resonances in the forced oscillators abstract in this paper we elaborate a refined analytical approach to study the subharmonic solutions as well as their bifurcation curves close to strong resonance points of order q 1 2 and 3 in the forced nonlinear oscillators therefore we propose to develop the higher order generalized averaging method to construct the approximations up to third order giving explicit formulas in the general case a process permitting the study of several resonances simultaneously is proposed furthermore for a class of forced nonlinear oscillators the existence possibility of two cycles of order q near resonance points which appear by saddle node bifurcations is shown the theoretical predictions of these bifurcations are tested by numerical integrations and very good agreement is found

a generic mechanism for spatiotemporal intermittency a simple mechanism for spatiotemporal intermittency is described it occurs in systems that exhibit bistability between a homogeneous stationary state and an oscillatory one close to parameter values where the oscillation disappears through an andronov homoclinic bifurcation c 1998 elsevier science b v all rights reserved

wrinkled tori and bursts due to resonant temporal forcing the effect of resonant temporal forcing on a system undergoing a hopf bifurcation with d4 square symmetry is studied the forcing breaks the continuous normal form symmetry of the governing amplitude equations but the d4 symmetry is preserved for this system it is shown that bursts with very large dynamic range may occur the bursts are associated with visits near solutions at infinity and are related to those found previously for the hopf bifurcation with broken d4 symmetry moehlis and knobloch physica d 135 2000 263 the regime in which an attracting quasiperiodic solution that exists in the absence of forcing wrinkles into chaos as the amplitude of the forcing increases is investigated in detail the overall behavior is governed by the approach of the resulting attractor to solutions at infinity windows with stable periodic solutions are found and associated with the traversal in parameter space through arnol d tongues other aspects of the dynamics are related to the presence of a new type of gluing bifurcation which we call a supergluing bifurcation 2001 elsevier science b v all rights reserved

the brezis ekeland principle for doubly nonlinear equations the celebrated brezis ekeland principle c r acad sci paris ser a b 282 1976 pp ai a1197 a1198 aii and a971 a974 characterizes trajectories of nonautonomous gradient flows of convex functionals as solutions to suitable minimization problems this note extends this characterization to doubly nonlinear evolution equations driven by convex potentials the characterization is exploited in order to establish approximation results for gradient flows doubly nonlinear equations and rate independent evolutions

front explosion in a resonantly forced complex ginzburg landau system abstract periodically forced oscillatory reaction diffusion systems near the hopf bifurcation can be modeled by the resonantly forced complex ginzburg landau equation in the 3 1 resonant locking regime this equation has three stable fixed points corresponding to the phase locked states in the underlying reaction diffusion system phase fronts separate spatial domains containing the phase locked states when the ginzburg landau equation parameters lie in the benjamin feir unstable regime the phase fronts have a turbulent internal spatio temporal structure as the forcing intensity is changed the intrinsic width of a front grows until at a critical value the front explodes and the turbulent interfacial zone expands to fill the entire domain the scaling properties of this transition are explored and it is shown that front width and spatial and temporal correlations diverge as the critical forcing intensity is approached these results are compared with similar behavior seen in a coupled map model with period 3 local dynamics the prospects for observation of these phenomena in experiments on periodically forced reaction diffusion systems are discussed

transition from oscillatory to excitable regime in a system forced at three times its natural frequency the effect of a temporal modulation at three times the critical frequency on a hopf bifurcation is studied in the framework of amplitude equations we consider a complex ginzburg landau equation with an extra quadratic term resulting from the strong coupling between the external field and the unstable modes we show that by increasing the intensity of the forcing one passes from an oscillatory regime to an excitable one with three equivalent frequency locked states in the oscillatory regime topological defects are one armed phase spirals while in the excitable regime they correspond to three armed excitable amplitude spirals analytical results show that the transition between these two regimes occurs at a critical value of the forcing intensity the transition between phase and amplitude spirals is confirmed by numerical analysis and it might be observed in periodically forced reaction diffusion systems

strictly nef divisors 0 introduction 565 1 basic definitions known results and main problems 567 2 results in case of non negative kodaira dimension 569 3 the albanese map 572 4 fano fibrations 575 5 birational maps 578 6 higher dimensions 583

existence results for doubly nonlinear higher order parabolic equations on unbounded domains on demontre un resultat d existence pour le probleme aux valeurs limites et initiales u q 1 sign u t a 1 u f sur 0 t q u satisfait des conditions de dirichlet sur 0 t u u 0 sur pour t 0 a 1 u 1 m m d d u p 1 sign d u pour p q 1 m n 1 et r n un ensemble ouvert

perturbation theory for domain walls in the parametric ginzburg landau equation we demonstrate that in the parametrically driven ginzburg landau equation arbitrarily small nongradient corrections lead to qualitative differences in the dynamical properties of domain walls in the vicinity of the transition from rest to motion these differences originate from singular rotation of the eigenvector governing the transition we present analytical results on the stability of ising walls deriving explicit expressions for the critical eigenvalue responsible for the transition from rest to motion we then develop a weakly nonlinear theory to characterize the singular character of the transition and analyze the dynamical effects of spatial inhomogeneities

on the evolution p laplacian with nonlocal memory abstract we study the homogeneous dirichlet problem for the evolution p laplacian with the nonlocal memory term 0 1 u t p u 0 t g t s p u x s d s x t u f x t in q 0 t where r n is a bounded domain g and f are given functions it is proved that for max 1 2 n n 2 p g g l 2 0 t and u 0 w 0 1 p f l 2 q the problem admits a weak solution which is global or local in time in dependence on the growth rate of x t s as s conditions of uniqueness are established it is proved that for p 2 and s x t s 0 the disturbances from the data propagate with finite speed and the waiting time effect is possible we present simple explicit solutions that show the failure of the maximum and comparison principles for the solutions of equation 0 1

time discretization and global solution for a doubly nonlinear volterra equation this note addresses the analysis of an abstract doubly nonlinear volterra equation with a nonsmooth kernel and possibly unbounded and degenerate operators by exploiting a suitable implicit time discretization technique we obtain the existence of a global strong solution as a by product the discrete scheme is proved to be conditionally stable and convergent

doubly nonlinear periodic problems with unbounded operators abstract the solvability of the evolution system v t b t u t f t v t a t u t 0 t t with the periodic condition v 0 v t is investigated in the case where a t are bounded possibly degenerate subdifferentials and b t are unbounded subdifferentials

self tuning to the hopf bifurcation in fluctuating systems the problem of self tuning a system to the hopf bifurcation in the presence of noise and periodic external forcing is discussed we find that the response of the system has a non monotonic dependence on the noise strength and displays an amplified response which is more pronounced for weaker signals the observed effect is to be distinguished from stochastic resonance for the feedback we have studied the unforced self tuned hopf oscillator in the presence of fluctuations exhibits sharp peaks in its spectrum the implications of our general results are briefly discussed in the context of sound detection by the inner ear

strong resonances of spatially distributed oscillators a laboratory to study patterns and defects abstract this paper describes phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing we show that the temporal forcing induces a new type of instability leading to the formation of spatial patterns such as stripes hexagons and spatio temporal intermittent states reminiscent of chemical and magnetical systems we also report the existence of localized states where the instability is confined in the core of a defect leading to an increased mobility and diffusive behaviour of the defect

collective chaos and noise in the globally coupled complex ginzburg landau equation abstract we study a globally coupled version of the complex ginzburg landau equation gc cgle which consists of a large number n of identical two dimensional oscillators coupled through their mean amplitude depending on parameter values different dynamical regimes are attained we focus particularly on an interesting regime where the individual oscillators follow erratic motion but in a sufficiently coherent way so that the average motion does not vanish when n becomes large and is also chaotic a simple description of this state is proposed by considering the motion of a single forced two dimensional system which has both a limit cycle and a fixed point as stable attractors determining which of these two deterministic attractors is selected by a weak noise and how this depends on the parameter of the reduced system allows us to determine self consistently the average amplitude and dominant frequency of the collective behaviour of the full system finally we show that adding a small noise to the gc cgle transforms the chaotic collective behaviour into a purely periodic one

two phase resonant patterns in forced oscillatory systems boundaries mechanisms and forms we use the forced complex ginzburg landau cgl equation to study resonance in oscillatory systems periodically forced at approximately twice the natural oscillation frequency the cgl equation has both resonant spatially uniform solutions and resonant two phase standing wave pattern solutions such as stripes or labyrinths the spatially uniform solutions form a tongueshaped region in the parameter plane of the forcing amplitude and frequency but the parameter range of resonant standing wave patterns does not coincide with the tongue of spatially uniform oscillations on one side of the tongue the boundary of resonant patterns is inside the tongue and is formed by the nonequilibrium ising bloch bifurcation and the instability to traveling waves on the other side of the tongue the resonant patterns extend outside the tongue forming a parameter region in which standing wave patterns are resonant but uniform oscillations are not the standing wave patterns in that region appear similar to those inside the tongue but the mechanism of their formation is different the formation mechanism is studied using a weakly nonlinear analysis near a hopf turing bifurcation the analysis also gives the existence and stability regions of the standing wave patterns outside the resonant tongue the analysis is supported by numerical solutions of the forced complex ginzburg landau equation 2004 elsevier b v all rights reserved

multiphase patterns in periodically forced oscillatory systems periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency we study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency the 4 1 resonance these systems possess four coexisting stable states corresponding to uniform oscillations with successive phase shifts of pi 2 using an amplitude equation approach near a hopf bifurcation to uniform oscillations we study front solutions connecting different phase states these solutions divide into two groups pi fronts separating states with a phase shift of pi and pi 2 fronts separating states with a phase shift of pi 2 we find a type of front instability where a stationary pi front open quotes decomposes close quotes into a pair of traveling pi 2 fronts as the forcing strength is decreased the instability is degenerate for an amplitude equation with cubic nonlinearities at the instability point a continuous family of pair solutions exists consisting of pi 2 fronts separated by distances ranging from zero to infinity quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability we conjecture the existence of similar instabilities in higher 2n 1 resonances n 3 4 hor ellipsis where stationarymore pi fronts decompose into ital n traveling pi n fronts the instabilities designate transitions from stationary two phase patterns to traveling 2n phase patterns as an example we demonstrate with a numerical solution the collapse of a four phase spiral wave into a stationary two phase pattern as the forcing strength within the 4 1 resonance is increased copyright ital 1999 ital the american physical society less

wavenumber locking and pattern formation in spatially forced systems we study wavenumber locking and pattern formation resulting from weak spatially periodic one dimensional forcing of two dimensional systems we consider systems that produce stationary or traveling stripe patterns when unforced and apply forcing aligned with the stripes forcing at close to twice the pattern wavenumber selects stabilizes or creates resonant stripes locked at half the forcing wavenumber if the mismatch between the forcing and pattern wavenumber is high we find that the pattern still locks but develops a wave vector component perpendicular to the forcing direction and forms rectangular and oblique patterns when the unforced system supports traveling waves resonant rectangular patterns remain stationary but oblique patterns travel in a direction orthogonal to the traveling waves

periodic forcing of a limit cycle oscillator fixed points arnold tongues and the global organization of bifurcations the effects of periodic pulsatile stimuli on a nonlinear limit cycle oscillation are analyzed for various relaxation rates to the limit cycle oscillation in the infinite relaxation limit the effects of periodic stimuli are analyzed by consideration of the bifurcations of circle maps in the case of a finite relaxation rate it is necessary to analyze two dimensional maps of the disk however the simple structure of the limit cycle allows us to carry out detailed theoretical and numerical analyses of the dynamics using the brouwer fixed point theorem we show that for any finite nonzero frequency and amplitude of the stimulus there will be a period 1 fixed point associated with a period 1 phase locking we use analytical and numerical methods to determine the stability boundary of the period 1 fixed point as a function of the stimulation frequency amplitude and relaxation rate to the limit cycle these results combined with numerical studies give insight into the changes in the global organization of the phase locking zones as a function of the relaxation rate to the limit cycle

nonsmooth data error estimates for approximations of an evolution equation with a positive type memory term we study the numerical approximation of an integro differential equation which is intermediate between the heat and wave equations the proposed discretization uses convolution quadrature based on the first and second order backward difference methods in time and piecewise linear finite elements in space optimal order error bounds in terms of the initial data and the inhomogeneity are shown for positive times without assumptions of spatial regularity of the data

a pseudo monotonicity adapted to doubly nonlinear elliptic parabolic equations the case where b is an unbounded linear operator was considered 1rst by bardos and br7 ezis 4 in the nonlinear case raviart 20 grange and mignot 13 dibenedetto and showalter 11 proved existence results assuming that a and b are at least monotone operators and b is compact alt and luckhaus 1 investigated the case of a non compact operator b assuming a is strongly monotone their work was extended more recently by ka cur 14 filo and ka cur 12 or zadrzy7 nska and zajb aczkowski 26 berm7 udez et al 7 devoted their work to the case where b is compact and strongly monotone and a is pseudo monotone we are interested in the same case excepted that b is no longer assumed to be strongly monotone thus the equation may

global characterization of the normal form for a vector field near a closed orbit on deduit une generalisation naturelle de la caracterisation globale de elphick pour des champs de vecteurs pres d une orbite fermee