on the structure of the set of bounded solutions on an almost periodic lienard equation abstract we study some properties of bounded solutions on 0 of the following almost periodic lienard equation x f x x g x p t where p r r is almost periodic function and g a b r is strictly decreasing function notably we describe the set of initial conditions of the bounded solutions on 0 and we state that these solutions are asymptotically almost periodic

existence and uniqueness of pseudo almost periodic solutions of recurrent neural networks with time varying coefficients and mixed delays this paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to recurrent delayed neural networks several conditions guaranteeing the existence and uniqueness of such solutions are obtained in a suitable convex domain furthermore several methods are applied to establish sufficient criteria for the globally exponential stability of this system the approaches are based on constructing suitable lyapunov functionals and the well known banach contraction mapping principle moreover the attractivity and exponential stability of the pseudo almost periodic solution are also considered for the system a numerical example is given to illustrate the effectiveness of our results

exponential stability of continuous time and discrete time cellular neural networks with delays convergence characteristics of continuous time cellular neural networks with discrete delays are studied by using lyapunov functionals we obtain delay independent sufficient conditions for the networks to converge exponentially toward the equilibria associated with the constant input sources halanay type inequalities are employed to obtain sufficient conditions for the networks to be globally exponentially stable it is shown that the estimates obtained from the halanay type inequalities improve the estimates obtained from the lyapunov methods discrete time analogues of the continuous time cellular neural networks are formulated and studied it is shown that the convergence characteristics of the continuous time systems are preserved by the discrete time analogues without any restriction imposed on the uniform discretization step size

erratum to existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients by combining the theory of the exponential dichotomy and liapunov function we study the existence and attractivity of almost periodic solutions for cellular neural networks cnns with distributed delays and variable coefficientsdx idt b i t x i t j 1 na i j t f j x j t j 1 nb i j t f j m j 0 k i j u x j t u du i i t we obtain some sufficient conditions to ensure that for the networks there exists a unique almost periodic solution and all its solutions converge to such an almost periodic solution an example is given to illustrate that the conditions of our results are feasible

almost periodic solutions of recurrent neural networks with continuously distributed delays abstract in this paper a class of recurrent neural networks with continuously distributed delays is discussed without resorting to the theory of exponential dichotomy several new sufficient conditions are obtained ensuring the existence of an almost periodic solution for this model based on a special functional and analysis technique moreover by constructing suitable lyapunov functions the attractivity and exponential stability of the almost periodic solution are also considered for the system the results obtained are helpful to design globally stable almost periodic oscillatory neural networks a numerical example is given to show the feasibility of the results obtained

dynamical behavior of vibro impact machinery near a point of codimension two bifurcation a dual component system with vibro impact is considered local codimension two bifurcation of maps involving a real eigenvalue and a complex conjugate pair escaping the unit circle simultaneously is analyzed by using the center manifold and normal form method for maps the period n single impact motion and poincare map of the vibro impact system are derived analytically stability and local bifurcation of single impact periodic motion are analyzed by using the poincare map a center manifold theorem technique is applied to reduce the poincare map to a three dimensional one and the normal form map associated with the codimension two bifurcation is obtained local behavior of the dual component system with vibro impact near the point of codimension two bifurcation is analyzed it is found that near the point of codimension two bifurcation there exists not only hopf bifurcation of period one single impact motion but also hopf bifurcation of period two double impact motion period doubling bifurcation of period one single impact motion commonly exists near the point of codimension two bifurcation however no period doubling cascade emerges due to change of the type of period two fixed points and occurrence of hopf bifurcation associated with period two fixed points the period two fixed points are symmetrical about the corresponding period one point the results from simulation show that the attracting invariant circles associated with period two points are symmetrical about the corresponding period one point near the value of hopf bifurcation of period two points two actual examples the impact forming machinery and inertial shaker are chosen to analyze further the phenomena of codimension two bifurcation of maps and local bifurcation analysis and numerical simulation are carried out to unfold dynamical behavior of these vibro impact systems near the points of codimension two bifurcations

existence and stability of almost periodic solution for bam neural networks with delays by using the banach fixed point theorem and constructing suitable lyapunov function some sufficient conditions are obtained ensuring existence uniqueness and global stability of almost periodic solution of the bam neural networks with variable coefficients and delays these results are helpful to design global exponential stable bam networks and almost periodic oscillatory bam networks

on compactly supported spline wavelets and a duality principle let v 1 v 0 v 1 be a multiresolution analysis of l 2 generated by the mth order b spline n m x we exhibit a compactly supported basic wavelet m x that generates the corresponding orthogonal complementary wavelet subspaces w 1 w 0 w 1 consequently the two finite sequences that describe the two scale relations of n m x and m x in terms of n m 2x j j z yield an efficient reconstruction algorithm to give an efficient wavelet decomposition algorithm based on these two finite sequences we derive a duality principle which also happens to yield the dual bases n m x j and 59 m x j relative to n m x j and m x j respectively

general approach to the localization of unstable periodic orbits in chaotic dynamical systems we present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system our approach allows us to locate in an efficient way the unstable cycles of in principle arbitrary length with a high accuracy based on a universal set of linear transformations the originally unstable periodic orbits are transformed into stable ones and can consequently be detected and analyzed easily this method is applicable to dynamical systems of any dimension and requires no preknowledges with respect to the solutions of the original chaotic system as an example of application of our method we investigate the ikeda attractor in some detail

existence and stability of almost periodic solutions for cellular neural networks with time varying delays in leakage terms on time scales abstract this paper is concerned with cellular neural networks with time varying delays in leakage terms on time scales some sufficient conditions on the existence uniqueness and global exponential stability of almost periodic solutions are established an example is presented to illustrate the feasibility and effectiveness of the obtained results

the birth of strange nonchaotic attractors abstract a mechanism is described for the development of strange nonchaotic attractors from two frequency quasiperiodic attractors in quasiperiodically driven maps this mechanism is intimately tied to the phenomenon of torus doubling the transition to strange nonchaotic behavior occurs when a period doubled torus collides with its unstable parent torus as the collision is approached the period doubled torus becomes extremely wrinkled ultimately becoming fractal at the collision the lyapunov exponent remains negative through the collision these collisions are shown to be a new type of attractor merging crisis the new feature is the possibility of nonchaotic attractors taking part in the crisis this mechanism is illustrated via numerical and analytical studies of a quasiperiodically driven logistic map

singular continuous spectra in dissipative dynamics we demonstrate the occurrence of regimes with singular continuous fractal fourier spectra in autonomous dissipative dynamical systems the particular example is an ordinary differential equation system at the accumulation points of bifurcation sequences associated with the creation of complicated homoclinic orbits two different mechanisms responsible for the appearance of such spectra are proposed in the first case when the geometry of the attractor is symbolically represented by the thue morse sequence both the continuous time process and its discrete poincar e map have singular power spectra the other mechanism is due to the logarithmic divergence of the first return times near the saddle point here the poincar e map possesses the discrete spectrum while the continuous time process displays the singular one a method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual fourier analysis technique

stagnation point von karman coefficient on the basis of various direct numerical simulations dns of turbulent channel flows the following picture is proposed i at a distance y from either wall the taylor microscale lambda is proportional to the average distance l s between stagnation points of the fluctuating velocity field i e lambda y b 1 l s y with b 1 constant for delta nu y or approximately equal to delta where the wall unit delta nu is defined as the ratio of kinematic viscosity nu to skin friction velocity u tau and delta is the channel s half width ii the number density n s of stagnation points varies with height according to n s c s delta nu 3 y 1 where y identical with y delta nu and c s is constant in the range delta nu y or approximately equal to delta iii in that same range the kinetic energy dissipation rate per unit mass equals 2 3 e u tau 3 kappa s y where e is the total kinetic energy per unit mass normalized by u tau 2 and kappa s b 1 2 c s is the stagnation point von karman coefficient iv in the limit of exceedingly large reynolds numbers re tau identical with delta delta nu large enough for the reynolds stress uv to equal u tau 2 in the range delta nu y delta and assuming that production of turbulent kinetic energy balances dissipation locally in that range and limit the mean velocity u normalized by u tau obeys d dy u approximately equal to 2 3 e kappa s y in that same range v it follows that the von karman coefficient kappa is a meaningful and well defined coefficient and the log law holds in turbulent channel pipe flows only if e is independent of y and re tau in that range in which case kappa approximately kappa s vi in support of d dy u approximately equal to 2 3 e kappa s y dns data of turbulent channel flows which include the highest currently available values of re tau are best fitted by e approximately equal to 2 3 b 4 y 2 15 and d dy u approximately equal to b 4 kappa s y 1 2 15 with b4 independent of y in delta nu y delta if the significant departure from uv approximately equal to u tau 2 at these re tau values is taken into account

some results on boundary value problems for fuzzy differential equations with functional dependence abstract we calculate the exact solution for a class of boundary value problems for first order linear fuzzy differential equations with impulses under hukuhara differentiability by finding green s function some conclusions can be derived for impulsive fuzzy differential equations including a term with functional dependence for which existence and uniqueness results are proved

efficient detection of periodic orbits in chaotic systems by stabilizing transformations an algorithm for detecting periodic orbits in chaotic systems r l davidchack and y c lai phys rev e 3 60 1999 pp 6172 6175 which combines the set of stabilizing transformations proposed by schmelcher and diakonos phys rev lett 78 1997 pp 4733 4736 with a modified semi implicit euler iterative scheme and seeding with periodic orbits of neighboring periods has been shown to be highly efficient when applied to low dimensional systems the difficulty in applying the algorithm to higher dimensional systems is mainly due to the fact that the number of the stabilizing transformations grows extremely fast with increasing system dimension here we analyze the properties of stabilizing transformations and propose an alternative approach for constructing a smaller set of transformations the performance of the new approach is illustrated on the four dimensional kicked double rotor map and the six dimensional system of three coupled henon maps

interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map mechanisms and their characterizations a simple quasiperiodically forced one dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors snas in a two parameter a ensuremath f space the routes include transitions to chaos via snas from both a one frequency torus and a period doubled torus in the former case we identify the fractalization and type i intermittency routes in the latter case we point out that at least four distinct routes for the truncation of the torus doubling bifurcation and the creation of snas occur in this model in particular the formation of snas through heagy hammel fractalization and type iii intermittent mechanisms is described in addition it has been found that in this system there are some regions in the parameter space where a dynamics involving a sudden expansion of the attractor which tames the growth of period doubling bifurcation takes place creating the sna the snas created through different mechanisms are characterized by the behavior of the lyapunov exponents and their variance by the estimation of the phase sensitivity exponent and through the distribution of finite time lyapunov exponents

hybrid spline frames using their unitary extension principle ron and shen have constructed a normalized tight frame for l 2 consisting of spline functions with uniform knots this paper constructs a normalized tight frame for l 2 0 oo comprising spline functions with knots on a hybrid of uniform and geometric mesh the construction is motivated by applications in adaptive approximation using spline functions on a hybrid mesh that admits a natural dyadic multiresolution approximation of l 2 0 based on dilation and translation

affine systems in l2 rd the analysis of the analysis operator abstract discrete affine systems are obtained by applying dilations to a given shift invariant system the complicated structure of the affine system is due first and foremost to the fact that it is not invariant under shifts affine frames carry the additional difficulty that they are global in nature it is the entire interaction between the various dilation levels that determines whether the system is a frame and not the behaviour of the system within one dilation level we completely unravel the structure of the affine system with the aid of two new notions the affine product and a quasi affine system this leads to a characterization of affine frames the induced characterization of tight affine frames is in terms of exact orthogonality relations that the wavelets should satisfy on the fourier domain several results such as a general oversampling theorem follow from these characterizations most importantly the affine product can be factored during a multiresolution analysis construction and this leads to a complete characterization of all tight frames that can be constructed by such methods moreover this characterization suggests very simple sufficient conditions for constructing tight frames from multiresolution of particular importance are the facts that the underlying scaling function does not need to satisfy any a priori conditions and that the freedom offered by redundancy can be fully exploited in these constructions an

torus doubling bifurcations and strange nonchaotic attractors in a vibro impact system whether strange nonchaotic attractors snas can occur typically in dynamical systems other than quasiperiodically driven systems has been an open problem here we show that the snas can be induced by the interruption of torus doubling bifurcation in a periodically driven vibro impact system it is found that the creation of snas occurs due to the collision of doubled torus with some unstable periodic orbits based on the poincare map technique two types of codimension 3 bifurcations are represented and typical torus doubling bifurcations can occur in the neighborhood of these bifurcation points we use the singular continuous fourier spectrum and its scaling to verify the strangeness nondifferentiability of the attractors the implicitly transcendental map is used to calculate the largest lyapunov exponent by qr based algorithm which ensures that the underlying dynamics with nonpositive lyapunov exponents is nonchaotic the associated mechanism is described for the creation of snas through detecting unstable periodic orbits from poincare map series

almost periodic solutions for cellular neural networks with time varying delays in leakage terms this paper concerns with cellular neural networks with time varying delays in leakage or forgetting terms without assuming boundedness on activation functions we establish sufficient conditions on existence and global exponential stability of almost periodic solutions by using lyapunov functional method and differential inequality techniques our results complement with some recent ones