a new rigorous expansion for the velocity potential of a circular piston source in the case of boundary value problems such as the sound scattering from a sphere placed in the nearfield of a plane piston source it is sometimes essential to express the velocity potentials in terms of the orthogonal expansion it is demonstrated in the present work that the rayleigh surface integral giving the velocity potential for a plane piston source surrounded by an infinite rigid flange reduces to a rigorous expansion of the simplest form for a circular piston as series of spherical surface harmonics the resulting equation is valid for any field points even on the piston surface sample calculations made with a microcomputer are presented with three dimensional and contour plots

parasite population delay model of malaria type with stochastic perturbation and environmental criterion for limitation of disease we present a stochastic delay model of an infectious disease malaria transmitted by a vectors mosquitoes after an incubation time a criterion for limitation of disease is found

global dynamics for a new high dimensional sir model with distributed delay abstract in this paper a new high dimensional sir epidemic model with double epidemic hypothesis and delays is proposed which is a high dimensional system of impulsive functional differential equations with time delays the linear chain trick technique is employed to prove the upper boundedness of solutions of the impulsive delay differential equations and scaling method techniques for inequalities and classification method are used to study the permanence of the high dimensional system we also prove that the infection free periodic solution of the system is globally attractive when r 1 1 and the system is permanent under r 2 1 moreover numerical simulation for impulsive and delayed system is presented to illustrate our main conclusions which shows that time delays and pulse vaccination have significant effects on the dynamics behaviors of the model the feature of the present paper is that the double epidemic hypothesis have different forms of delays to more realistically describe the spread of epidemic though which makes the high dimensional system more complex

when coherent stochastic resonance appears we consider a system driven by a combination of gaussian white noise and a periodic signal it is demonstrated when the mean exit time for this system necessarily exhibits a minimum as a function of the frequency of the periodic bias and gives rise to the phenomenon known as coherent stochastic resonance this reasoning begins by calculating an exact expression for the mean exit time of a system driven by noise and a telegraph signal and showing that no resonancelike behavior arises this unexpected result lets us identify the sufficient conditions for resonance to appear the origin of coherent stochastic resonance lies in the different behavior of low frequency and high frequency periodic signals

dynamic behavior for a nonautonomous sirs epidemic model with distributed delays a nonautonomous sirs epidemic model with distributed delay is investigated two new threshold values r and r are derived the model is permanent as r 1 and r 1 implies the extinction of the disease using the liapunov functional method global behavior of the model is studied

a study of the fokker planck equation of bistable systems by the method of state dependent diagonalization we study the fokker planck equation of one dimensional bistable systems with symmetric as well as asymmetric potentials in this work the method of state dependent diagonalization sdd is proposed for solving the eigenvalue problem of the associated schrodinger equation the example of a quartic bistable potential is used to illustrate its validity unlike the conventional exact diagonalization the sdd method is found to be quite efficient for the high eigenstates we use the eigenfunctions and eigenvalues obtained by this method to calculate the propagator the spectral density of the autocorrelation function and the response of the system to a weak periodic driving force for various noise intensities the asymmetry of the potential is found to play an important role and it strongly influences the signal to noise ratio

traveling waves for a diffusive sir model with delay abstract in this paper we study traveling waves connecting the infection free equilibrium state and the endemic equilibrium state for a diffusive sir model with delay and saturated incidence rate since this system does not enjoy the comparison principle we will use an iteration process to construct a pair of upper and lower solutions with the aid of the pair of upper and lower solutions we can apply the schauder fixed point theorem to construct a family of solutions of the truncated problems which via the limiting argument can generate the traveling wave indeed we show that there exists c 0 such that this system admits a traveling wave solution with speed c iff c c

global stability of a delayed sir epidemic model with density dependent birth and death rates an sir epidemic model with density dependent birth and death rates is formulated in our model it is assumed that the total number of the population is governed by logistic equation the transmission of infection is assumed to be of the standard form namely proportional to i t h n t h where n t is the total variable population size i t is the size of the infective population and a time delay h is a fixed time during which the infectious agents develop in the vector we consider transmission dynamics for the model stability of an endemic equilibrium is investigated the stability result is stated in terms of a threshold parameter that is a basic reproduction number r 0

on axis and far field sound radiation from resilient flat and dome shaped radiators on axis and far field series expansions are developed for the sound pressure due to an arbitrary circular symmetric velocity distribution on a flat radiator in an infinite baffle these expansions are obtained by expanding the velocity distributions in terms of orthogonal polynomials r 2n 0 sigma a p n 2 sigma a 2 1 with p n the legendre polynomials the terms r 2n 0 give rise to a closed form expression for the pressure on axis as well as for the far field pressure furthermore for a large number of velocity profiles including those associated with the rigid piston the simply supported radiator and the clamped radiators as well as gaussian radiators there are closed form expressions for the required expansion coefficients in particular for the rigid simply supported and clamped radiators this results in explicit finite series expressions for both the on axis and far field pressures in the reverse direction a method of estimating velocity distributions from measured on axis pressures by matching in terms of expansion coefficients is proposed together with the forward far field computation scheme this yields a method for far field loudspeaker assessment from on axis data generalized keele scheme the forward computation scheme is extended to dome shaped radiators with arbitrary velocity distributions

an annular superposition integral for axisymmetric radiators a fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators this method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the rayleigh sommerfeld integral or the generalized king integral expressions are derived for plane circular pistons using both continuous wave and pulsed excitations several commonly used apodization schemes for the surface velocity distribution are considered including polynomial functions and a smooth piston function the effect of different apodization functions on the spectral content of the wave field is explored quantitative error and time comparisons between the new method the rayleigh sommerfeld integral and the generalized king integral are discussed at all error levels considered the annular superposition method achieves a speed up of at least a factor of 4 relative to the point source method and a factor of 3 relative to the generalized king integral without increasing the computational complexity

the low frequency axisymmetric modal sound radiation efficiency of an elastically supported annular plate abstract this paper deals with the sound radiation efficiency of a vibrating thin elastically supported annular plate embedded into a flat rigid baffle the free axisymmetric time harmonic vibrations have been considered for a single mode it has been assumed that the influence of the air column above the plate on the plate s vibrations is negligible first the sound radiation efficiency has been formulated as an integral further rigorous mathematical manipulations have been carried out based on the theory of summation of multiple expansion series containing the hypergeometric functions as a result the formulations have been expressed as some fast convergent expansion series containing only the bessel and struve functions of integer order and the spherical bessel functions the presented formulations of sound radiation efficiency of an elastically supported annular plate are useful for numerical calculations within the low frequency range what is important for practical reasons the formulations are valid for axisymmetric boundary conditions and they enable changing the values of boundary stiffness constants consequently the analysis of influence of the plate s edge attachment on the sound radiation efficiency has been performed the limiting transitions have also been performed from formulations valid for the elastically supported annular plates to the formulations valid for annular plates with classical boundary conditions clamped simply supported and free at one edge or at both edges

threshold and stability results for an age structured seir epidemic model abstract in this paper an age structured seir epidemic model is considered the existence and uniqueness of a positive solution for this model is proved threshold results for the existence of endemic states are established under certain conditions the local stability for the steady states is also examined

ultrasonic field modeling by distributed point source method for different transducer boundary conditions several investigators have modeled ultrasonic fields in front of transducers by huygens fresnel superposition principle that integrates the contributions of a number of point sources distributed on the transducer face this integral solution also known as the rayleigh integral or rayleigh sommerfeld integral solution assumes the strengths of the point sources distributed over the transducer face a newly developed technique called distributed point source method dpsm offers an alternative approach for modeling ultrasonic fields dpsm is capable of modeling the field for prescribed source strength distribution as well as for prescribed interface conditions with unknown source strengths it is investigated how the ultrasonic field in front of the transducer varies in different situations 1 when the point source strengths are known 2 when the point source strengths are unknown but obtained from the interface condition that only the normal component of the transducer velocity is continuous across th

on the short wave acoustic radiation from planar panels or beams of rectangular shape an exact representation which involves single as opposed to double integrals is established for the time average power output generated by individual modes of normal surface velocity on a simply supported and baffled rectangular panel fluid loading is not taken into account the representation enables analytical estimates to be found in the short wavelength range and provides details hitherto unresolved by numerical analysis

complete global analysis of a two scale network sirs epidemic dynamic model with distributed delay and random perturbations the model validation results are established the basic reproduction numbers at three human vector contact levels are computed the stochastic stability of equilibria is proven interplay between stability and human mobility are exhibited in real life scenarios a stochastic sirs epidemic dynamic model with distributed time delay for vector borne diseases in two scale network structured populations is presented the distributed delay accounts for the varying incubation period of the disease furthermore the disease dynamics is influenced by random environmental perturbations in the disease transmission process as well as the two scale human mobility process the basic reproduction numbers at three human vector contact levels in the two scale population are computed and the results for the stochastic asymptotic stability of the equilibria are presented moreover the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented numerical simulation results are presented

coherent stochastic resonance in a sextic double well potential abstract we study the response of a stochastic system described by the one dimensional fokker planck equation with a sextic double well potential u 6 x c 4 x 4 c 6 x 6 to a weak sinusoidal periodic signal two types of boundary conditions have been investigated i absorbing boundary conditions and ii natural boundary conditions the unperturbed propagators are calculated by the eigenfunction expansion method we find that for case i the mean survival time shows the coherent stochastic resonance and for case ii the signal to noise ratio exhibits the stochastic resonance the results are compared with those of the bistable quartic double well potential u 4 x 1 2 x 2 1 4 x 4

accumulating regions of winding periodic orbits in optically driven lasers we investigate the route to locking in class b lasers subject to optically injected light for injection strengths and detunings near a codimension two saddle node hopf point this is the parameter region where the adler approximation is not valid and where yeung and strogatz recently reported a self similar cascade of periodic orbits in the case of a solid state laser we explain this cascade as an accumulation of large regions bounded by saddle node bifurcations of periodic orbits but also containing further bifurcations such as period doubling torus bifurcations and small pockets of chaos in the vicinity of the simultaneous saddle node and hopf bifurcations successive periodic orbits wind more and more near the point in phase space where the saddle node bifurcation is about to occur this leads to a self similar period adding cascade by varying the linewidth enhancement parameter from zero the case of a solid state or co2 laser to values larger than 1 the case of semiconductor lasers we show how the accumulating regions of winding periodic orbits change rapidly this explains why the period adding cascade has not been found in injected semiconductor lasers moreover we are able to identify certain regions with complex dynamics in injected semiconductor lasers as remainders of the accumulating regions 2002 elsevier science b v all rights reserved

on the sound field of a circular membrane in free space and an infinite baffle an enhanced method for calculating the radiation characteristics of a tensioned circular membrane in free space is presented using an analytical solution to the infinite integral in the free space green s function in cylindrical coordinates this enables direct calculation of the surface pressure series coefficients by equating the coefficients of the resulting bessel series in a set of simultaneous equations eliminating both numerical integration and least squares minimization improves calculation speed and accuracy an infinite baffle is introduced to provide an indication of what the theoretical limit of the bass performance would be using a very large enclosure furthermore analytical solutions to the pressure field integrals are presented a force transmission coefficient is introduced which is the ratio of the total radiation impedance to the motional impedance the motional radiation and diaphragm impedances of the damped membrane are calculated together with the near and far field pressure responses and efficiency a comparison is made between the on axis response without damping calculated using this method and using a finite element model it is demonstrated that good correlation between the two calculation methods can be achieved provided the elements are small enough and a sufficiently large model is used at the frequency extremes

simplified expansions for radiation from a baffled circular piston computation of acoustic radiation from a baffled circular piston continues to be an active area of investigation both as a canonical problem and because of numerous practical applications for time harmonic radiation exact series expansions are an attractive approach because they do not require numerical integration or limiting approximations here series expansions due to hasegawa inoue and matsuzawa j acoust soc am 74 1044 1047 1983 75 1048 1051 1984 are shown to reduce to simpler expressions suitable for numerical computations for the region r a where a is the piston radius and r is the distance from the piston center an exact solution is given by a series of spherical hankel functions and legendre polynomials with explicit closed form position independent coefficients for the paraxial region w a where w is the distance from the piston axis a second exact series expansion is valid for all axial distances z and reduces to the known analytic solution for w 0 these two expansions allow the radiated field to be computed at any point with rapid convergence except for points near the circle bounding the piston example numerical results illustrate application of this method to ultrasonic sources

a collocation method for the gurtin maccamy equation with finite life span a collocation method along the characteristics for a stiff problem arising from population dynamics is proposed and analyzed it is a fourth order implicit runge kutta method of two stage to the integration of the ode along the characteristics whose collocation points are zeros of the linearly transformed legendre monic polynomial nonnegativity of the numerical solutions is shown the stability of the method is discussed it is proven that the scheme is convergent at a fourth order rate in the maximum norm several numerical examples are presented

stability analysis of delayed sir epidemic models with a class of nonlinear incidence rates we analyze stability of equilibria for a delayed sir epidemic model in which population growth is subject to logistic growth in absence of disease with a nonlinear incidence rate satisfying suitable monotonicity conditions the model admits a unique endemic equilibrium if and only if the basic reproduction number r0 exceeds one while the trivial equilibrium and the disease free equilibrium always exist first we show that the disease free equilibrium is globally asymptotically stable if and only if r0 1 second we show that the model is permanent if and only if r0 1 moreover using a threshold parameter r0 characterized by the nonlinear incidence function we establish that the endemic equilibrium is locally asymptotically stable for 1 r0 r0 and it loses stability as the length of the delay increases past a critical value for 1 r0 r0 our result is an extension of the stability results in j j wang j z zhang z jin analysis of an sir model with bilinear incidence rate nonl anal rwa 11 2009 2390 2402

on the sound field of a resilient disk in an infinite baffle the rayleigh integral describing the near field pressure of an axisymmetric planar monopole source with an arbitrary velocity distribution is solved with a method similar to that used by mast and yu j acoust soc am 118 6 3457 3464 2005 for a rigid disk in an infinite baffle the closed form solution is in the form of a double expansion which is valid for distances from the observation point to the center of the source that are greater than its radius however for the remaining immediate near field the king integral is solved using a combination of gegenbauer s summation theorem and the lommel expansion resulting in a solution which is in the form of a triple expansion reducing to a double expansion along the source s axis of symmetry these relatively compact solutions in analytic form do not require numerical integration and therefore present no numerical difficulties except for a singularity at the rim as an example of a monopole source with an arbitrary velocity distribution equations

coherent stochastic resonance in a system with in out intermittency abstract we study the effect of noise on the properties of in out intermittency we add noise to a single variable of the system the one parallel to the invariant subspace at some magnitude of noise a new kind of coherent stochastic resonance is observed in which the average time spent near the invariant subspace has a maximum as a function of the magnitude of the noise we present numerical simulations of this phenomenon and a simple theoretical model using a markov chain

anin vacuo modal expansion method to determine the transient response of fluid loaded planar vibrators abstract a general approach is presented to evaluate the vibratory response of fluid loaded planar vibrators to broadband time dependent excitations for either radiation or scattering problems the velocity of the vibrator is expressed as a sum of the products of thein vacuo modes and the time dependent modal velocities in contrast to thein vacuo case the modal velocities are coupled due to fluid loading a set of coupled convolution integral equations for the time dependent modal velocities is developed and rearranged to facilitate their numerical solution analytical expressions are obtained for the impulse responses of thepc fluid loaded admittances these impulse responses which are the modal velocities when thepc or high frequency approximation is made for the effect of fluid loading are then used to compute the modal velocities when the effect of coupling is included since the known terms in the coupled convolution integral equations are very easily obtained a large number of modes can be included in the analysis numerical results are presented to illustrate the effect of coupling on the velocity responses of simply supported plates to convecting line excitations and clamped circular plates to impacts

a radial propagator for axisymmetric pressure fields the concept of a propagator is central to the angular spectrum formulation of diffraction theory which expresses the pressure field diffracted by a two dimensional aperture as a superposition of a continuum of plane waves in the conventional form an exponential term known as a propagator is multiplied by the wavenumber spectrum obtained from a two dimensional spatial fourier transform of the aperture boundary condition to obtain the wavenumber spectrum in a plane parallel to the boundary offset by some distance specified in the propagator by repeated use of this propagator and fourier inversion it is possible to completely construct the homogeneous part of the pressure field in the positive half space beyond the planar boundary containing the aperture drawing upon preceding work relating the boundary condition to the axial pressure pees j acoust soc am 127 3 1381 1390 2010 it is shown in this article that when the aperture is axially symmetric an alternative type of propagator can b

a general formulation for the sound radiation from rectangular baffled plates with arbitrary boundary conditions the radiation of sound from a baffled rectangular plate with edges elastically restrained against deflection and rotation is analyzed the elastic constants along the contour can be varied to reproduce simply supported clamped free or guided edges as limiting cases the formulation is based on a variational method for the vibration of the plate and assumes no fluid loading of the structure the elastic boundary conditions appear in the hamiltonian of the plate through a dynamic contribution which is expressed in terms of nondimensional edge parameters the extremalization of the hamiltonian is achieved using a rayleigh ritz method and both the free vibrations and the forced vibrations of the plate are presented the radiation of sound from the plate is analyzed in the far field and is calculated from one dimensional fourier transforms numerical results are presented for the radiation efficiency of modes of simply supported clamped free and guided plates the values found agree well with predic

global stability of a delayed sirs epidemic model with saturation incidence and temporary immunity in this paper a delayed sirs epidemic model with saturation incidence and temporary immunity is investigated the immunity gained by experiencing a disease is temporary whenever infected the diseased individuals will return to the susceptible class after a fixed period by analyzing the corresponding characteristic equations the local stability of an endemic equilibrium and a disease free equilibrium is discussed by comparison arguments it is proved that if the basic reproduction number is less than unity the disease free equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity by means of an iteration technique sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium numerical simulations are carried out to illustrate the main theoretical results

theoretical analysis of sound radiation of an elastically supported circular plate abstract this study focuses on the analysis of the active and reactive sound power of the axisymmetric modes of free vibrations of elastically supported circular plates embedded in a rigid baffle some linear and time harmonic processes have been considered it is assumed that the plate radiates some acoustic waves into a hemisphere filled with a lossless gaseous medium the integral formulations for the active and reactive sound power have been derived and expressed in their hankel representations they have been used to derive some elementary formulations in the form of some high frequency asymptotes valid for frequencies higher than the successive coincidence frequencies of the plate therefore the discussion on some sample numerical results mostly covers the sound power radiated at those frequencies the asymptotes are easy to express in a computer code and they do not need great processor capacity they are therefore useful for engineering use the main benefit of the analysis presented in this paper is that the sound power for all the possible boundary configurations of the boundary stiffnesses i e classical clamped guided simply supported or completely free boundaries as well as all the intermediate situations has been described using the same formulae this is possible simply by changing the two values of stiffnesses associated with the boundary conditions whose influence on the radiated sound power has been discussed the solution of the problem of sound power radiated by a vibrating elastically supported circular plate presented herein is essentially more general than the solutions presented earlier for the classical boundary configurations such as clamped simply supported guided or completely free circular plates

analysis of an improved epidemic model with stochastic disease transmission abstract this paper proposes an improved logistic epidemic model and carries out the complete parameters analysis of asymptotic behavior of infectious diseases some interesting details such as the threshold value of outbreak of epidemics and critical states of disease spread are derived the mean and variance of proportion of infected population are given explicitly the results show that our model is more reasonable and applicable to describe the real situation especially p 1 2 might be considered as the alarm for relate institutions to make effective policies to prevent and control some epidemics

the normalized acoustic power of a thin clamped annular plate vibrating in a flat screen around a perpendicular semi infinite circular cylinder abstract the neumann boundary value problem is presented for the time harmonic excited steady state vibrations of a thin clamped annular plate embedded in a flat rigid baffle around a perpendicular circular cylindrical rigid semi infinite baffle the system of two coupled differential equations is solved for this purpose one of them being the wave equation of the fluid filling the space between the two baffles and the other being the equation of motion of the plate for its excited vibrations first the acoustic pressure is presented in its spectral form using the weber inverse transform then the time averaged acoustic power is presented using the plate s modal impedance coefficients and the coupling factors the modal coefficients are presented as the integrals together with the corresponding asymptotic formulations the influence of the cylindrical baffle on the acoustic power is analyzed numerically the fluid loading and the internal attenuation of the plate s vibrations are both included whereas the attenuation of the acoustic waves in fluid is neglected

a joint wavenumber time domain technique to determine the transient acoustic radiation loading on planar vibrators abstract a new method is presented to determine the transient radiation loading on planar vibrators mounted on rigid infinite baffles by using a wave vector time domain technique the specified non uniform velocity of the vibrator is expressed as a time dependent modal expansion where the modes are solutions to the homogeneous problem the time dependent acoustic modal forces can then be expressed as a sum of the modal radiation impulse responses convolved with the modal velocities in order to evaluate the radiation impulse responses the relationship between the fourier and hankel transforms of circular symmetric functions is first used to express the green s function for the problem as an integral over wave vector space the integral form of the green s function is then used to reduce the expression for the radiation impulse responses from a double surface integral over the vibrator to an integral over the wave vector space in contrast to the double surface integral which is difficult to evaluate the integral over the wave vector space can be evaluated easily numerical results are presented for clamped circular plates and simply supported square plates

numerical implementation of the lumped parameter model for the acoustic power output of a vibrating structure in a previous paper a lumped parameter model for the acoustic radiation from a vibrating structure was defined by dividing the surface of the structure into elements expanding the acoustic field from each of the elements in a multipole expansion and truncating all but the lowest order terms in the expansion here the lumped parameter model is implemented numerically by requiring the boundary condition for the normal surface velocity to be satisfied in a lumped parameter sense this alleviates the difficulties typically encountered in enforcing the boundary condition leading to a relatively simple numerical solution with well defined convergence properties the basis functions for the numerical analysis are taken as the acoustic fields of discrete simple dipole and tripole sources located at the geometrical centers of the surface elements the different source types are used to represent the radiation from different kinds of surface elements simple sources for elements in the plane of an infinite baffle dipole sources for very thin structures which deform only in bending and tripole sources for elements associated with parts of a structure enclosing a finite volume the convergence of the numerical solution for the power output as a function of both frequency and element size is demonstrated through several example problems

permanence of an sir epidemic model with density dependent birth rate and distributed time delay abstract in this paper we investigate the permanence of an sir epidemic model with a density dependent birth rate and a distributed time delay we first consider the attractivity of the disease free equilibrium and then show that for any time delay the delayed sir epidemic model is permanent if and only if an endemic equilibrium exists numerical examples are given to illustrate the theoretical analysis the results obtained are also compared with those from the analog system with a discrete time delay

asymptotic formulas for the acoustic radiation impedance of an elastically supported annular plate this paper deals with the normalized acoustic radiation impedance of an elastically supported annular plate in axisymmetric vibrations cauchy s theorem about residues and the stationary phase method have been used to approximate the corresponding integrals as a result elementary asymptotic formulas valid for axisymmetric boundary configurations of clamped guided simply supported and free annular plates as well as for all the intermediate boundary configurations have been obtained

global stability of an sir epidemic model with constant infectious period in this paper we derive and study an sir epidemic model with constant infectious period which is incorporated as a time delay both trivial and endemic equilibrium are found and their stability is investigated using lyapunov functional approach sufficient conditions for global stability of endemic equilibrium is obtained

influence of noise on scalings for in out intermittency we study the effects of noise on a recently discovered form of intermittency referred to as in out intermittency this type of intermittency which reduces to on off in systems with a skew product structure has been found in the dynamics of maps ode and pde simulations that have symmetries it shows itself in the form of trajectories that spend a long time near a symmetric state interspersed with short bursts away from symmetry in contrast to on off intermittency there are clearly distinct mechanisms of approach towards and away from the symmetric state and this needs to be taken into account in order to properly model the long time statistics we do this by using a diffusion type equation with a delay integral boundary condition this model is validated by considering the statistics of a two dimensional map with and without the addition of noise

dynamics of a discretized sir epidemic model with pulse vaccination and time delay we derive a discretized sir epidemic model with pulse vaccination and time delay from the original continuous model the sufficient conditions for global attractivity of an infection free periodic solution and permanence of our model are obtained improving discretization our results are corresponding to those in the original continuous model

two state intermittency near a symmetric interaction of saddle node and hopf bifurcations a case study from dynamo theory we consider a model of a hopf bifurcation interacting as a codimension 2 bifurcation with a saddle node on a limit cycle motivated by a low order model for magnetic activity in a stellar dynamo this model consists of coupled interactions between a saddle node and two hopf bifurcations where the saddle node bifurcation is assumed to have global reinjection of trajectories the model can produce chaotic behaviour within each of a pair of invariant subspaces and also it can show attractors that are stuck on to both of the invariant subspaces we investigate the detailed intermittent dynamics for such an attractor investigating the effect of breaking the symmetry between the two hopf bifurcations and observing that it can appear via blowout bifurcations from the invariant subspaces we give a simple markov chain model for the two state intermittent dynamics that reproduces the time spent close to the invariant subspaces and the switching between the different possible invariant subspaces this clarifies the observation that the proportion of time spent near the different subspaces depends on the average residence time and also on the probabilities of switching between the possible subspaces

the sound power of an individual mode of a clamped free annular plate abstract the main aim of this study is an analysis of sound radiation of some clamped free and free clamped annular plates the plates are embedded in some infinite perfectly rigid baffles and vibrate with the free field condition satisfied the kirchhoff love linear theory of a perfectly elastic plate is used to solve the plates equations of motion the sound pressure at the plates surfaces is expressed by its hankel transform the closed path integral technique known from the literature and the stationary phase method are used to find the standardized active and reactive sound power of an individual mode in the form of some high frequency asymptotic formulae useful for some highly efficient engineering computations their non oscillating and oscillating parts have been separated it is assumed that the vibration and sound radiation are axisymmetric and time harmonic low fluid loading is also assumed the complex sound power of an individual mode forms the basis for computing the total sound power of some excited and damped vibrations in the fluid the total sound power is not discussed in this study

hybrid stabilization and synchronization of nonlinear systems with unbounded delays the stabilization of nonlinear systems with bounded and unbounded time delays via hybrid control is studied we investigate and identify switching rules for which stabilization can be verified a priori when this approach is inadequate stabilizing state dependent switching rules are constructed this method is based on partitioning the state space into switching regions unwanted physical behavior such as chattering and zeno behavior is avoided sufficient conditions are established using razumikhin like theorems the theoretical results provide insight into how hybrid control strategies can be constructed to synchronize a class of nonlinear systems with unbounded delay the findings are illustrated through numerical simulations

cycling chaos its creation persistence and loss of stability in a model of nonlinear magnetoconvection we examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets this cycling chaos manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets interspersed with short transitions between neighbourhoods of these sets such behaviour is robust to perturbations that preserve the symmetry of the system we examine bifurcations of this state we discuss a scenario where an attracting cycling chaotic state is created at a blowout bifurcation of a chaotic attractor in an invariant subspace this differs from the standard scenario for the blowout bifurcation in that in our case the blowout is neither subcritical nor supercritical the robust cycling chaotic state can be followed to a point where it loses stability at a resonance bifurcation and creates a series of large period attractors the model we consider is a ninth order truncated ordinary differential equation ode model of three dimensional incompressible convection in a plane layer of conducting fluid subjected to a vertical magnetic field and a vertical temperature gradient symmetries of the model lead to the existence of invariant subspaces for the dynamics in particular there are invariant subspaces that correspond to regimes of two dimensional flows with variation in the vertical but only one of the two horizontal directions stable two dimensional chaotic flow can go unstable to three dimensional flow via the cross roll instability we show how the bifurcations mentioned above can be located by examination of various transverse liapunov exponents we also consider a reduction of the ode to a map and demonstrate that the same behaviour can be found in the corresponding map this allows us to describe and predict a number of observed transitions in these models the dynamics we describe is new but nonetheless robust and so should occur in other applications

splitting methods for the numerical approximation of some models of age structured population dynamics and epidemiology splitting methods for nonlinear models arising from population dynamics and epidemiology are described and analyzed a backward finite differencing along the characteristic is used for the approximation it is shown that the schemes are convergent at first order rate in the maximum norm the stability of the methods is discussed several numerical examples are presented

an epidemic model of a vector borne disease with direct transmission and time delay abstract this paper considers an epidemic model of a vector borne disease which has direct mode of transmission in addition to the vector mediated transmission the incidence term is assumed to be of the bilinear mass action form we include both a baseline ode version of the model and a differential delay model with a discrete time delay the ode model shows that the dynamics is completely determined by the basic reproduction number r 0 if r 0 1 the disease free equilibrium is globally stable and the disease dies out if r 0 1 a unique endemic equilibrium exists and is locally asymptotically stable in the interior of the feasible region the delay in the differential delay model accounts for the incubation time the vectors need to become infectious we study the effect of that delay on the stability of the equilibria we show that the introduction of a time delay in the host to vector transmission term can destabilize the system and periodic solutions can arise through hopf bifurcation

stability of synchronous chaos and on off intermittency in coupled map lattices in this paper we consider the stability of synchronous chaos in lattices of coupled n dimensional maps for global coupling we derive explicit conditions for computing the parameter values at which the synchronous chaotic attractor becomes unstable and bifurcates into asynchronous chaos in particular we show that after the bifurcation one generally observes on off intermittency a process in which the entire system evolves nearly synchronously but chaotically for long periods of time which are interrupted by brief bursts away from synchrony for nearest neighbor coupled systems however we show that the stability of the synchronous chaotic state is a function of the system size in particular for large systems we will not be able to observe synchronous chaos we derive a condition relating the local map s largest lyapunov exponent to the maximal system size under which one can still observe synchronous chaos and on off intermittency other issues related to the characterization of on off intermittent signals are also discussed

backward bifurcation of an epidemic model with saturated treatment function an epidemic model with saturated incidence rate and saturated treatment function is studied here the treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals is getting larger and the medical condition is limited the global dynamics of the model indicate that the basic reproduction number being the unity is a strict threshold for disease eradication when such effect is weak however it is shown that a backward bifurcation will take place when this delayed effect for treatment is strong therefore driving the basic reproduction number below the unity is not enough to eradicate the disease and a critical value at the turning point is deduced as a new threshold some sufficient conditions for the disease free equilibrium and the endemic equilibrium being globally asymptotically stable are also obtained mathematical results in this paper suggest that giving the patients timely treatment improving the cure efficiency and decreasing the infective coefficient are all valid methods for the control of disease

global analysis of an infection age model with a class of nonlinear incidence rates abstract sir infection age models with a very general class of nonlinear incidence rates f s j are investigated we give a necessary and sufficient condition for global asymptotic stability of the free equilibrium related to the basic reproduction number furthermore additional conditions allow us to prove an exponential stability of this disease free equilibrium finally by using a lyapunov functional we show the global asymptotic stability of the endemic equilibrium whenever it exists

comparison of spheroidal and eigenfunction expansion trial functions for a membrane in an infinite baffle the on axis far field pressure response of a circular membrane in an infinite baffle when driven by a uniformly distributed electrostatic force is calculated using two different trial functions for the surface velocity distribution the first is an expansion based upon a solution to the free space wave equation in oblate spheroidal coordinates which has already been derived in a previous paper j acoust soc am 120 5 2460 2477 2006 and the second is a membrane eigenfunction expansion or bessel series which is rigorously derived in this letter although the latter can be used as a basis for calculating a number of different radiation characteristics such as the radiation impedance or directivity etc only the on axis far field sound pressure is considered here the results are compared and discussed

approximation of the struve function h1 occurring in impedance calculations the problem of the rigid piston radiator mounted in an infinite baffle has been studied widely for tutorial as well as for practical reasons the resulting theory is commonly applied to model a loudspeaker in the audio frequency range a special function the struve function h 1 z occurs in the expressions for the rigid piston radiator this struve function is not readily available in programs such as matlab or mathcad nor in computer languages such as fortran and c therefore a simple and effective approximation of h 1 z which is valid for all z is developed some examples of the application of the struve function in acoustics are presented

endemic threshold results for an age structured sis epidemic model with periodic parameters abstract the main contribution of this paper is to obtain a threshold value for the existence and uniqueness of a nontrivial endemic periodic solution of an age structured sis epidemic model with periodic parameters under the assumption of the weak ergodicity of a non autonomous lotka mckendrick system we formulate a normalized system for an infected population as an initial boundary value problem of a partial differential equation the existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on a banach space of locally integrable periodic l 1 valued functions we prove that the spectral radius of the frechet derivative of the integral operator at zero plays the role of a threshold for the existence and uniqueness of a nontrivial fixed point of the operator corresponding to a nontrivial periodic solution of the original differential equation in a weak sense if the malthusian parameter of the host population is equal to zero our threshold value is equal to the well known epidemiological threshold value the basic reproduction number r 0 however if it is not the case then two threshold values are different from each other and we have to pay attention on their actual biological implications

multiple epidemic waves in delayed susceptible infected recovered models on complex networks we consider a delayed susceptible infected recovered epidemic model on an uncorrelated complex network and address the effect of time lag on the shape and multiple waves of epidemic curves we show that when the transmission rate is above a threshold a large delay can cause multiple waves with larger amplitudes in the second and subsequent waves

fokker planck equation and subdiffusive fractional fokker planck equation of bistable systems with sinks abstract we study the dynamics of stochastic systems obeying the one dimensional diffusive fokker planck equation fpe as well as systems described by the subdiffusive fractional fokker planck equation sffpe with a confining potential u x and in the presence of delta function sinks for the one sink and two sink problems we obtain exact expressions for the laplace transform of the propagator p and derive several asymptotic results for the survival probability s p and the survival time distribution f the decay rate constants of the diffusive system are also analyzed we apply our method to a bistable system with a quartic double well potential and calculate p s p and f of the corresponding fpe and sffpe for different strengths and positions of the sink s finally we derive asymptotic expressions of s p and f for the subdiffusive system which are valid for a general u x and a general sink distribution