almost sure exponential stability of numerical solutions to stochastic delay hopfield neural networks stability of numerical solutions to stochastic delay differential equations have received an increasing attention but there has been so far little work on the stability analysis of numerical solutions to stochastic delay hopfield neural networks the aim of this paper is to study the almost sure exponential stability of numerical solutions to stochastic delay hopfield neural networks by using two approaches the euler method and the backward euler method under some reasonable conditions both the euler scheme and the backward euler scheme are proved to be almost sure exponential stability in particular the euler method and the backward euler method are mainly based on the semimartingale convergence theorem

lasalle type theorem and its applications to infinite horizon optimal control of discrete time nonlinear stochastic systems based on discrete martingale theory the lasalle type theorem for general discrete time stochastic systems is obtained and the almost sure stability is in turn discussed as applications infinite horizon nonlinear optimal regulator is investigated and a dynamical programming equation called the hamilton jacobi bellman equation is also derived for discrete time nonlinear stochastic optimal control

new criterion of partial asymptotic stability in probability of stochastic differential equations autonomous system of stochastic differential equations dx t f x dt i 1 kg i x dw i t which has a zero solution x 0 is considered it is assumed that there exists a positive definite with respect to part of the variables function v x such that corresponding operator lv is nonpositive it is proved that if the set m 0 x lv 0 x v x 0 does not include entire semitrajectories of the system 2 1 almost surely then the zero solution is asymptotically stable in probability with respect to part of the variables

on brockett s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback the necessity of brockett s condition for stabilizability of nonlinear systems by smooth feedback is shown by an argument based on properties of a degree for set valued maps to persist when the class of controls is enlarged to include discontinuous feedback

a refinement of matrosov s theorem for differential inclusions this note presents a refinement of matrosov s theorem for a class of differential inclusions whose set valued map is defined as a closed convex hull of finitely many vector fields this class of systems may arise in the analysis of switched nonlinear systems when stability with arbitrary switching between the given vector fields is considered assuming uniform global stability of a compact set it is shown that uniform global attractivity of the set can be verified by tailoring matrosov functions to individual vector fields this refinement of matrosov s theorem is an extension of the existing matrosov results which may be easier to apply to certain differential inclusions than existing results as demonstrated by an example

stability criteria of random nonlinear systems and their applications stochastic differential equations sdes are widely adopted to describe systems with stochastic disturbances while they are not necessarily the best models in some specific situations this paper considers the nonlinear systems described by random differential equations rdes the notions and the corresponding criteria of noise to state stability asymptotic gain and asymptotic stability are proposed in the m th moment or in probability several estimation methods of stochastic processes are presented to explain the reasonability of the assumptions used in theorems as applications of stability criteria some examples about stabilization regulation and tracking are considered respectively a theoretical framework on stability of rdes is finally constructed which is distinguished from the existing framework of sdes

a note on persistence and extinction of a randomized food limited logistic population model this paper addresses the issue of the asymptotic behavior for a non autonomous randomized food limited logistic population model several sufficient conditions are formulated and proved for p moment persistence and extinction of the population as well as in sense of almost sure results show that food limited assumption has an influence on the convergence rate of the solution to the equilibria for the deterministic and stochastic model some previously known results are improved numerical simulations are provided to support the results

plus minus p adic l functions for hilbert modular forms abstract r pollack constructed in pollack 2003 13 plus minus p adic l functions for elliptic modular forms which are p adically bounded when the hecke eigenvalues at p are zero the most supersingular case the goal of this work is to generalize his construction to hilbert modular forms we find a suitable condition for hilbert modular forms corresponding to the vanishing of p th hecke eigenvalue in elliptic modular form case which guarantees the existence of plus minus p adic l functions which are p adically bounded as an application we construct cyclotomic plus minus p adic l functions for modular elliptic curves over a totally real field f under the assumption that a p e 0 for each prime p dividing p we formulate a cyclotomic plus minus iwasawa main conjecture for such elliptic curves

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

stochastic versions of the lasalle theorem the main aim of this paper is to establish stochastic versions of the well known lasalle stability theorem from these stochastic versions follow many classical results on stochastic stability this shows clearly the power of our new results

existence and uniqueness theorems for periodic markov process and applications to stochastic functional differential equations abstract this work is devoted to an m valued markov process with a periodic transition probability function where m is a polish space sufficient conditions for the existence and uniqueness of the periodic markov process are given these existence theorems are rather general and the corresponding results in 1 11 15 23 are improved and generalized the uniqueness theorems for the periodic markov process are original as applications we study the existence uniqueness and global attractivity of periodic solution for the periodic stochastic n species lotka voltrra competitive model with bounded delays and the periodic stochastic neural networks with infinite delay respectively numerical simulations are presented to illustrate the main results

a nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems a new infinitesimal sufficient condition is given for uniform global asymptotic stability ugas for time varying nonlinear systems it is used to show that a certain relaxed persistency of excitation condition called uniform spl delta persistency of excitation u spl delta pe is sufficient for uniform global asymptotic stability in certain situations u spl delta pe of the right hand side of a time varying differential equation is also shown to be necessary under a uniform lipschitz condition the infinitesimal sufficient condition for ugas involves the inner products of the flow field with the gradients of a finite number of possibly sign indefinite locally lipschitz lyapunov like functions these inner products are supposed to be bounded by functions that have a certain nested or triangular negative semidefinite structure this idea is reminiscent of a previous idea of matrosov who supplemented a lyapunov function having a negative semidefinite derivative with an additional function having a derivative that is definitely nonzero where the derivative of the lyapunov function is zero for this reason we call the main result a nested matrosov theorem the utility of our results on stability analysis is illustrated through the well known case study of the nonholonomic integrator

the main conjecture for cm elliptic curves at supersingular primes at a prime of ordinary reduction the iwasawa main conjecture for elliptic curves relates a selmer group to a p adic l function in the supersingular case the statement of the main conjecture is more complicated as neither the selmer group nor the p adic l function is well behaved recently kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is similar in structure to the ordinary case namely kobayashi s conjecture relates modified selmer groups which he defined with modified padic l functions defined by the first author in this paper we prove kobayashi s conjecture for elliptic curves with complex multiplication

the improved lasalle type theorems for stochastic functional differential equations abstract the main aim of this paper is to improve some results obtained by mao x mao the lasalle type theorems for stochastic functional differential equations nonlinear stud 7 2000 307 328 our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above for example we need only the local lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions to guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation sfde under the weaker conditions imposed in this paper we establish a generalised existence and uniqueness theorem which covers a wider class of nonlinear sfdes as demonstrated by the examples discussed in this paper moreover from our improved results follow some new criteria on the stochastic asymptotic stability for sfdes

iwasawa theory of elliptic curves at supersingular primes over ℤ p extensions of number fields in this paper we make a study of the iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary zp extension of a number field k in the case when p splits completely in k generalizing work of kobayashi 9 and perrin riou 17 we define restricted selmer groups and invariants we then derive asymptotic formulas describing the growth of the selmer group in terms of these invariants to be able to work with non cyclotomic zp extensions a new local result is proven that gives a complete description of the formal group of an elliptic curve at a supersingular prime along any ramified zp extension of qp

stability in distribution of neutral stochastic functional differential equations with markovian switching abstract stability in distribution of stochastic differential equations with markovian switching and stochastic differential delay equations with markovian switching have been studied by several authors and this kind of stability is an important property for stochastic systems there are several papers which study this stability for stochastic differential equations with markovian switching and stochastic differential delay equations with markovian switching technically in our paper we are concerned with the general neutral stochastic functional differential equations with markovian switching and we derive the sufficient conditions for stability in distribution at the end of our paper one example is established to illustrate the theory of our work

the almost sure asymptotic stability and p th moment asymptotic stability of nonlinear stochastic differential systems with polynomial growth this note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems sdss the systems coefficients are assumed to satisfy local lipschitz condition and polynomial growth condition by applying some novel techniques some easily verifiable conditions are obtained which ensure the almost sure asymptotic stability and pth moment asymptotic stability for such sdss we also provide the range of the order p a numerical example is provided to illustrate the effectiveness and the benefits of the proposed result

p th moment noise to state stability of stochastic differential equations with persistent noise this paper studies the stability properties of stochastic differential equations subject to persistent noise including the case of additive noise which is noise that is present even at the equilibria of the underlying differential equation and does not decay with time the class of systems we consider exhibit disturbance attenuation outside a closed not necessarily bounded set we identify conditions based on the existence of lyapunov functions to establish the noise to state stability in probability and in pth moment of the system with respect to a closed set as part of our analysis we study the concept of two functions being proper with respect to each other formalized via a pair of inequalities with comparison functions we show that such inequalities define several equivalence relations for increasingly strong refinements on the comparison functions we also provide a complete characterization of the properties that a pair of functions must satisfy to belong to the same equivalence class th

dissipativity theory for nonlinear stochastic dynamical systems in this paper we develop stochastic dissipativity theory for nonlinear dynamical systems using basic input output and state properties specifically a stochastic version of dissipativity using both an input output as well as a state dissipation inequality in expectation for controlled markov diffusion processes is presented the results are then used to derive extended kalman yakubovich popov conditions for characterizing necessary and sufficient conditions for stochastic dissipativity of stochastic dynamical systems using two times continuously differentiable storage functions in addition feedback interconnection stability in probability results for stochastic dynamical systems are developed thereby providing a generalization of the small gain and positivity theorems to stochastic systems

an embedded boundary method for the wave equation with discontinuous coefficients a second order accurate embedded boundary method for the two dimensional wave equation with discontinuous wave propagation speed is described the wave equation is discretized on a cartesian grid with constant grid size and the interface across which the wave speed is discontinuous is allowed to intersect the mesh in an arbitrary fashion by using ghost points on either side of the interface previous embedded boundary techniques for the neumann and dirichlet problems are generalized to satisfy the jump conditions across the interface to second order accuracy the resulting discretization of the jump conditions has the desirable property that each ghost point can be updated independently of all other ghost points resulting in a fully explicit time integration method we prove that the one dimensional restriction of the method is stable without damping for arbitrary locations of the interface relative to the grid for the two dimensional case the previously developed fourth order a t a dissipation is generalized to handle jump conditions we demonstrate that this operator provides sufficient stabilization to enable long time simulations while being weak enough to preserve the accuracy of the solution numerical examples are given where the method is used to study electromagnetic scattering of a plane wave by a dielectric cylinder the numerical solutions are evaluated against the analytical solution due to mie and pointwise second order accuracy is confirmed

isogeometric boundary element for analyzing steady state heat conduction problems under spatially varying conductivity and internal heat source abstract this paper proposes an isogeometric boundary element igabem with the aim to solve the 2d steady state heat conduction problems under spatially varying conductivity and internal heat source the igabem boundary domain integral equation is derived underlying the divergence theorem of gauss and the laplace equation the non uniform rational b spline nurbs basis used in the cad cae industries is applied to approximate both the boundary of problem domain and the unknown physical quantities and the radial integration method rim is employed to deal with the domain integrals induced by the non homogeneous thermal conductivity and the internal heat source the present boundary domain integral equation is firstly divided into several nurbs patches upon which the igabem can be further defined the main advantage of the nurbs basis in comparison with the standard piecewise polynomial basis is that there is almost no error in the boundary approximation with igabem which plays a significant role in controlling the accuracy of numerical calculation four numerical examples consisting of square regions with cubic and exponential thermal conductivities with or without internal heat source annulus region with constant and quadratic conductivities as well as complex region with varying thermal conductivity and complex heat source are provided the accuracy and convergence of the proposed method are assessed by comparing the present solution with the existing results obtained by several other researchers or ansys results and excellent performance is achieved

almost sure exponential stability of numerical solutions for stochastic delay differential equations using techniques based on the continuous and discrete semimartingale convergence theorems this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations sddes the important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of sddes directly this is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the chebyshev inequality and the borel cantelli lemma

some contributions to stochastic asymptotic stability and boundedness via multiple lyapunov functions most of the existing results on stochastic stability use a single lyapunov function but we shall instead use multiple lyapunov functions in this paper to establish some sufficient criteria for locating the limit sets of solutions of stochastic differential equations from them follow many useful results on stochastic asymptotic stability and boundedness which enable us to construct the lyapunov functions much more easily in applications in particular the well known classical theorem on stochastic asymptotic stability is a special case of our more general results these show clearly the power of our new results

nested matrosov function theorem for nonlinear delayed systems abstract in this paper the stability problem for time varying nonlinear delayed systems is investigated an infinite dimensional version of the nested matrosov function theorem is proposed to conclude uniform global asymptotic stability for time varying nonlinear delayed systems such a stability theorem requires a weak lyapunov functional and some auxiliary functionals and the upper bounds of the derivatives on these functionals must satisfy some nested conditions the proposed results can be used to analyze uniform asymptotic stability of time varying delayed systems where lasalle s invariance principle cannot be applied and barbalat s lemma is not sufficient to conclude the uniform attractivity property an example is given to illustrate the effectiveness of the proposed stability theorem

a posteriori error analysis of the crank nicolson finite element method for linear parabolic interface problems a reconstruction approach abstract this article studies a residual based a posteriori error analysis for the crank nicolson time stepping finite element method for a linear parabolic interface problem in a bounded convex polygonal domain in r 2 a piecewise linear finite element space is used in space that is allowed to change in time and a modified crank nicolson approximation is applied for the time discretizations we employ a space time reconstruction that is piecewise quadratic in time and the clement type interpolation estimates to derive optimal order in time and an almost optimal order in space a posteriori error bound in the l l 2 norm the interface is assumed to be of arbitrary shape but is of class c 2 for our purpose numerical results are presented to validate the derived estimators

lyapunov based adaptive state estimation for a class of nonlinear stochastic systems this paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters these nonlinear systems have a linear in parameter structure and the nonlinearity is assumed to be bounded in a lipschitz like manner using stochastic counterparts of lyapunov stability theory we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous time and discrete time nonlinear stochastic systems sufficient conditions are given in terms of the solvability of lmis moreover we also introduce a suboptimal design approach to optimizing the upper bound of the mean square error of parameter estimation this suboptimal design procedure is also realized by lmi computations by a martingale method we also show that the related lyapunov function has a non negative lyapunov exponent

global stability and stochastic permanence of a non autonomous logistic equation with random perturbation abstract this paper discusses a randomized non autonomous logistic equation d n t n t a t b t n t d t t d b t where b t is a 1 dimensional standard brownian motion in d q jiang n z shi a note on non autonomous logistic equation with random perturbation j math anal appl 303 2005 164 172 the authors show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0 we show that this equation is stochastically permanent and the solution n p t is globally attractive provided a t b t and t are continuous t periodic functions a t 0 b t 0 and min t 0 t a t max t 0 t 2 t by the way the similar results of a generalized non autonomous logistic equation with random perturbation are yielded

a recurrence principle for stochastic difference inclusions the invariance principle is extended to a recurrence principle and is developed for stochastic difference inclusions for these systems random solutions are not unique under appropriate lyapunov like conditions it is established for every random solution that almost every complete sample path converges to the largest weakly totally recurrent set contained in a level set of the lyapunov like function such a set is not larger and is sometimes smaller than the largest weakly invariant set contained in the level set the principle is useful for establishing robust uniform asymptotic stability in probability or robust uniform strong recurrence under weak lyapunov conditions for stochastic discrete time control systems that employ discontinuous feedback laws examples demonstrate the achieved results

stabilization of input disturbed stochastic port hamiltonian systems via passivity it is a universal phenomenon that the inputs of a real stochastic process are disturbed however this phenomenon is often ignored when stochastic port hamiltonian system sphs is used for modeling in which only the disturbance on the states is considered for this reason an extension of sphs named input disturbed sphs id sphs is proposed to describe the inputs disturbance as well as the states one the definition and some properties of id sphs including structure invariance and stochastic passivity are presented one by one to construct the basic framework of id sphs based on this framework a passivity based controller is further developed to stabilize id sphs at its steady state the control strategy is demonstrated in a thermodynamic heat conduction process with the results supporting strongly the proposed id sphs theory

stochastic periodic solution for a perturbed non autonomous predator prey model with generalized nonlinear harvesting and impulses abstract in this paper stochastic non autonomous predator prey models with and without impulses are investigated the effects of generalized nonlinear harvesting for prey and predator populations are considered for the stochastic system without impulses the existence and uniqueness of the positive solution is proven and sufficient conditions that guarantee the extinction and persistence of the population in the mean are achieved we show the existence of a nontrivial positive periodic solution by constructing appropriate lyapunov functions and using khasminskii s theory moreover the global attractiveness and stochastic persistence in probability of the stochastic model are discussed results show that the stronger noises and nonlinear harvesting component can significantly influence the dynamics of the system and lead to the extinction of the predator population additionally for the stochastic predator prey system with impulsive effect we prove that there exists a positive periodic solution numerical simulations are conducted to show the effectiveness and feasibility of the obtained results

asymptotic stability in hybrid systems via nested matrosov functions a theorem on nested matrosov functions is extended to time varying hybrid systems it provides sufficient conditions for uniform global asymptotic stability of a compact set an application to parameter identification with state resets is made and illustrated on an example

almost sure stabilizability of controlled degenerate diffusions we develop a direct lyapunov method for the almost sure open loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes the infinitesimal decrease condition for a lyapunov function is a new form of hamilton jacobi bellman partial differential inequality of second order we give local and global versions of the first and second lyapunov theorems assuming the existence of a lower semicontinuous lyapunov function satisfying such an inequality in the viscosity sense an explicit formula for a stabilizing feedback is provided for affine systems with smooth lyapunov function several examples illustrate the theory

a domain decomposition method for the acoustic wave equation with discontinuous coefficients and grid change a domain decomposition technique is proposed for the computation of the acoustic wave equation in which the bulk modulus and density fields are allowed to be discontinuous at the interfaces inside each subdomain the method presented coincides with the second order finite difference schemes traditionally used in geophysical modeling however the possibility of assigning to each subdomain its own space step makes numerical simulations much less expensive another interest of the method lies in the fact that its hybrid variational formulation naturally leads to exact equations for gridpoints on the interfaces transposing babuska brezzi s formalism on mixed and hybrid finite elements provides a suitable functional framework for this domain decomposition formulation and shows that the inf sup condition remains the basic requirement for convergence to occur

brief paper small gain control method for stochastic nonlinear systems with stochastic iiss inverse dynamics this paper investigates the small gain type conditions on stochastic iiss siiss systems and makes full use of these conditions in the design and analysis of the controller the contributions are as follows 1 a new proof of the stochastic lasalle theorem is provided 2 the small gain type conditions on siiss are developed and their relationship is discussed 3 based on the stochastic lasalle theorem and siiss small gain type conditions the adaptive controllers are designed to guarantee that all of the closed loop signals are bounded almost surely and the stochastic closed loop systems are globally asymptotically stable in probability

feedback control of quantum state reduction feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement we formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter we explore the use of stochastic lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability

a converse lyapunov theorem and robustness for asymptotic stability in probability a converse lyapunov theorem is established for discrete time stochastic systems with non unique solutions in particular it is shown that global asymptotic stability in probability implies the existence of a continuous lyapunov function smooth outside of the attractor that decreases in expected value along solutions the keys to this result are mild regularity conditions imposed on the set valued mapping that characterizes the update of the system state and the ensuing robustness of global asymptotic stability in probability to sufficiently small state dependent perturbations

a lyapunov theorem certifying global weak reachability for stochastic difference inclusions with random inputs abstract in this paper a lyapunov condition certifying global weak reachability of a compact set is given for stochastic set valued discrete time systems with respect to such systems under mild regularity assumptions it is shown that the existence of a lower semicontinuous function that decreases in expected value for at least one measurable selection from the set valued mapping outside a compact set is a sufficient condition for global weak reachability of such a set

a matrosov theorem for adversarial markov decision processes matrosov s relaxation of lyapunov conditions for uniform global asymptotic stability in time varying systems is extended to stochastic set valued discrete time systems nested matrosov functions are used to give conditions for stability that complement invariance principles for time invariant systems unlike invariance principles matrosov functions also can be applied to general time varying systems

strong convergence and stability of implicit numerical methods for stochastic differential equations with non globally lipschitz continuous coefficients we are interested in the strong convergence and almost sure stability of euler maruyama em type approximations to the solutions of stochastic differential equations sdes with non linear and non lipschitzian coefficients motivation comes from finance and biology where many widely applied models do not satisfy the standard assumptions required for the strong convergence in addition we examine the globally almost surely asymptotic stability in this non linear setting for em type schemes in particular we present a stochastic counterpart of the discrete lasalle principle from which we deduce stability properties for numerical methods

a class of stochastic delayed sir epidemic models with generalized nonlinear incidence rate and temporary immunity abstract a class of sir epidemic model with generalized nonlinear incidence rate is presented in this paper temporary immunity and stochastic perturbation are also considered the existence and uniqueness of the global positive solution is achieved sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established moreover the threshold behavior is discussed and the threshold value r 0 is obtained we show that if r 0 1 the disease eventually becomes extinct with probability one whereas if r 0 1 then the system remains permanent in the mean

attraction stability and robustness for stochastic functional differential equations with infinite delay this paper establishes the stochastic lasalle theorem to locate limit sets for stochastic functional differential equations with infinite delay from which some criteria on attraction boundedness stability and robustness are obtained to illustrate the applications of our results clearly this paper considers a scalar stochastic integro differential equation with infinite delay as an example

convergence of finite element methods for hyperbolic heat conduction model with an interface abstract the paper concerns numerical study of non fourier bio heat transfer model in multi layered media specifically we employ the maxwell cattaneo equation on the physical media with discontinuous coefficients a fitted finite element method is proposed and analyzed for a hyperbolic heat conduction model with discontinuous coefficients typical semidiscrete and fully discrete schemes are presented for a fitted finite element discretization with straight interface triangles the fully discrete space time finite element discretizations are based on second order in time newmark scheme optimal a priori error estimates for both semidiscrete and fully discrete schemes are proved in l l 2 norm numerical experiments are reported for several test cases to confirm our theoretical convergence rate finite element algorithm presented here can be used to solve a wide variety of hyperbolic heat conduction models for non homogeneous inner structures

lyapunov and converse lyapunov theorems for stochastic semistability abstract this paper develops lyapunov and converse lyapunov theorems for stochastic semistable nonlinear dynamical systems semistability is the property whereby the solutions of a stochastic dynamical system almost surely converge to not necessarily isolated lyapunov stable in probability equilibrium points determined by the system initial conditions specifically we provide necessary and sufficient lyapunov conditions for stochastic semistability and show that stochastic semistability implies the existence of a continuous lyapunov function whose infinitesimal generator decreases along the dynamical system trajectories and is such that the lyapunov function satisfies inequalities involving the average distance to the set of equilibria

a converse lyapunov theorem for strong global recurrence abstract a converse lyapunov theorem is established for discrete time stochastic systems modeled by a set valued mapping under mild regularity conditions for this class of systems it is shown that strong global recurrence is a necessary and sufficient condition for the existence of a smooth lyapunov function that decreases in expected value along solutions outside of the set that is strongly globally recurrent robustness of strong global recurrence to sufficiently small perturbations is also established

finite element methods and their convergence for elliptic and parabolic interface problems in this paper we consider the finite element methods for solving second order elliptic and parabolic interface problems in two dimensional convex polygonal domains nearly the same optimal l 2 norm and energy norm error estimates as for regular problems are obtained when the interfaces are of arbitrary shape but are smooth though the regularities of the solutions are low on the whole domain the assumptions on the finite element triangulation are reasonable and practical

analysis of a stochastic non autonomous food limited lotka volterra cooperative model in this paper a stochastic non autonomous food limited lotka volterra cooperative model is proposed and investigated sufficient conditions are formulated and verified for p moment persistence and extinction of the system results demonstrate that cooperative coefficients have important effects on the convergence rate of the solution to the equilibria of the stochastic model some numerical simulations are introduced to support the analytical results

asymptotic stability and smooth lyapunov functions abstract we establish that differential inclusions corresponding to upper semicontinuous multifunctions are strongly asymptotically stable if and only if there exists a smooth lyapunov function since well known concepts of generalized solutions of differential equations with discontinuous right hand side can be described in terms of solutions of certain related differential inclusions involving upper semicontinuous multifunctions this result gives a lyapunov characterization of asymptotic stability of either filippov or krasovskii solutions for differential equations with discontinuous right hand side in the study of weak as opposed to strong asymptotic stability the existence of a smooth lyapunov function is rather exceptional however the methods employed in treating the strong case of asymptotic stability are applied to yield a necessary condition for the existence of a smooth lyapunov function for weakly asymptotically stable differential inclusions this is an extension to the context of lyapunov functons of brockett s celebrated covering condition from continuous feedback stabilization theory

on the p adic l function of a modular form at a supersingular prime in this paper we study the two p adic l functions attached to a modular form f sum a sb nq sp n at a supersingular prime p when a sb p 0 we are able to decompose both the sum and the difference of the two unbounded distributions attached to f into a bounded measure and a distribution that accounts for all of the growth moreover this distribution depends only upon the weight of f and the fact that a sb p vanishes from this description we explain how the p adic l function is controlled by two iwasawa functions and by two power series with growth which have a fixed infinite set of zeros theorem 5 1 asymptotic formulas for the p part of the analytic size of the tate shafarevich group of an elliptic curve in the cyclotomic direction are computed using this result these formulas compare favorably with results established by m kurihara in 11 and b perrin riou in 23 on the algebraic side moreover we interpret kurihara s conjectures on the galois structure of the tate shafarevich group in terms of these two iwasawa functions

iwasawa theory for elliptic curves at supersingular primes we give a new formulation in iwasawa theory for elliptic curves at good supersingular primes this formulation is similar to mazur s at good ordinary primes namely we define a new selmer group and show that it is of cotorsion then we formulate the iwasawa main conjecture as that the characteristic ideal is generated by pollack s p adic l function we show that this main conjecture is equivalent to kato s and perrin riou s main conjectures we also prove an inequality in the main conjecture by using kato s euler system in terms of the and the invariants of our selmer group we specify the numbers and in the asymptotic formula for the order of the tate shafarevich group by kurihara and perrin riou

equivalent characterizations of input to state stability for stochastic discrete time systems input to state stability iss for stochastic difference inclusions is studied first iss in probability relative to a compact set is defined subsequently several equivalent characterizations are given for example iss in probability is shown to be equivalent to global asymptotic stability in probability when the disturbance takes values in a ball whose radius is determined by a sufficiently small but unbounded function of the distance of the state to the compact set in turn a recent converse lyapunov theorem for global asymptotic stability in probability provides an equivalent lyapunov characterization finally robust iss in probability is defined and is shown to give another equivalent characterization

discrete time stochastic control systems a continuous lyapunov function implies robustness to strictly causal perturbations abstract discrete time stochastic systems employing possibly discontinuous state feedback control laws are addressed allowing discontinuous feedbacks is fundamental for stochastic systems regulated for instance by optimization based control laws we introduce generalized random solutions for discontinuous stochastic systems to guarantee the existence of solutions and to generate enough solutions to get an accurate picture of robustness with respect to strictly causal perturbations under basic regularity conditions the existence of a continuous stochastic lyapunov function is sufficient to establish that asymptotic stability in probability for the closed loop system is robust to sufficiently small state dependent strictly causal worst case perturbations robustness of a weaker stochastic stability property called recurrence is also shown in a global sense in the case of state dependent perturbations and in a semiglobal practical sense in the case of persistent perturbations an example shows that a continuous stochastic lyapunov function is not sufficient for robustness to arbitrarily small worst case disturbances that are not strictly causal our positive results are also illustrated by examples

stability theorems for delay differential inclusions this technical note addresses stability problems of delay differential inclusions a chain rule is proposed for a wide class of lyapunov krasovskii functionals which are not necessarily invariantly differentiable we also obtain an invariance like theorem where the derivative of the candidate functional is bounded above by a continuous negative semidefinite function several examples are given to show the effectiveness of the results

global stability and stabilization of more general stochastic nonlinear systems abstract this paper considers the global stability and stabilization of more general stochastic nonlinear systems due to the absence of the conventional assumptions e g lipschitz condition the stochastic nonlinear systems under investigation may have more than one weak solution however the most associated results are only applicable to the stochastic systems having a unique strong solution and therefore it is meaningful to refine and extend the relevant concepts and methods to the more general case in this paper the concepts of stochastic stability in the more general sense are first introduced to cover the stochastic nonlinear systems having more than one weak solution then the generalized stochastic barbashin krasovskii theorem and lasalle theorem are established which present the criterions of stochastic stability for more general stochastic nonlinear systems as one of the main contributions in this paper we rigorously prove the generalized stochastic barbashin krasovskii theorem moreover based on the generalized theorems the output feedback and state feedback stabilization are accomplished respectively for two classes of high order stochastic nonlinear systems under rather weaker assumptions comparing to the existing literature

a matrosov theorem for strong global recurrence a theorem on nested matrosov functions is presented for time varying stochastic set valued discrete time systems satisfying mild regularity conditions it establishes sufficient conditions for uniform strong global recurrence of an open bounded set in general matrosov functions are required to satisfy less rigid requirements than typical lyapunov functions that satisfy a strict decrease condition along trajectories

explicit conditions for asymptotic stability of stochastic lienard type equations with markovian switching this paper deals with the boundedness in probability and convergence for solutions of stochastic lienard type equations some explicit conditions to ensure that all solution is bounded in probability and convergent to some fixed sets are obtained we also show that white noise can affect the boundedness of corresponding deterministic lienard equations

matrosov theorem for parameterized families of discrete time systems a version of matrosov s theorem for parameterized discrete time time varying systems is presented the theorem is a discrete time version of the continuous time result in loria et al 2002 d persistency of excitation a necessary and sufficient condition for uniform attractivity 2002 submitted for publication our result facilitates controller design for sampled data nonlinear systems via their approximate discrete time models an application of the theorem to establishing uniform asymptotic stability of systems controlled by model reference adaptive controllers designed via approximate discrete time plant models is presented

recurrence principles and their application to stability theory for a class of stochastic hybrid systems in this paper we establish results similar in nature to the invariance principle for a class of stochastic hybrid systems modeled by set valued mappings in particular we characterize the set to which bounded random solutions converge in terms of a new concept called weak total recurrence a refinement of the result under the existence of a non increasing on average lyapunov like function is also established a comparison between weak total recurrence and the frequently studied invariance concepts are presented finally application of the main results to establish weak sufficient conditions for certifying stochastic stability properties like uniform global asymptotic stability in probability for compact sets and uniform global recurrence for open bounded sets are discussed

stochastic barbalat s lemma and its applications in the deterministic case a significant improvement on stability analysis of nonlinear systems is caused by introducing barbalat s lemma into control area after lyapunov s second method and lasalle s theorem were established this note considers the extension of barbalat s lemma to the stochastic case to this end the uniform continuity and the absolute integrability are firstly described in stochastic forms it is nevertheless a small generalization upon the existing references since our result can be used to adapted processes which are not necessarily ito diffusions when it is applied to ito diffusion processes many classical results on stochastic stability are covered as special cases

practical asymptotic stability of stochastic systems driven by levy processes and its application to control of tora systems two lyapunov type theorems are developed to investigate global practical asymptotic stability in probability for sdes driven by non vanishing levy processes which can be either affine or non a

global stability analysis for stochastic coupled systems on networks this paper considers the global stability problem for some stochastic coupled systems on networks scsns we provide a systematic method for constructing a global lyapunov function for these scsns by using graph theory and the lyapunov second method consequently a new global stability principle which has a close relation to the topology property of the network is given as an application to the results we employ the principle to two well known coupled systems in physical and ecology and then some easy verified sufficient conditions which guarantee the global stability are obtained

existence uniqueness and global asymptotic stability of positive solutions of a predator prey system with holling ii functional response with random perturbation abstract this paper discusses a randomized two species predator prey system with holling ii functional response we show that the positive solution of the associated stochastic delay differential equation does not explode to infinity in a finite time in addition the existence uniqueness and global asymptotic stability of the positive solutions are studied

verification of lyapunov functions for the analysis of stochastic lienard equations versions of stochastic lienard equations perturbed by both additive and multiplicative white noise are considered we discuss existence uniqueness continuity boundedness and moment stability of solutions with the help of several lyapunov type functions the lyapunov functions are explicitly found to control uniform moment boundedness and stability a new matching condition on the interaction of resistance and restoring force plays an essential role to guarantee stability uniform boundedness of p th moments by validation of those lyapunov functions

the asymptotic stability and exponential stability of nonlinear stochastic differential systems with markovian switching and with polynomial growth abstract this paper discusses the asymptotic stability and exponential stability of nonlinear stochastic differential systems with markovian switching sdswmss the systems coefficients are assumed to satisfy local lipschitz condition and polynomial growth condition by applying some novel techniques we propose some conditions under which such sdswmss are asymptotically stable and exponentially stable nontrivial examples are provided to illustrate our results