stochastic suppression and stabilization of functional differential equations abstract without the linear growth condition or the one sided linear growth condition this paper discusses whether or not stochastic noise feedback can stabilize a given unstable nonlinear functional system x t f x t t since f may defy the linear growth condition or the one sided linear growth condition this system may explode in a finite time to stabilize this system this paper stochastically perturbs this system into the stochastic functional differential system d x t f x t t d t q x t d w 1 t x t x t d w 2 t by two independent brownian motions w 1 t and w 2 t this paper shows that the brownian motion w 2 t may suppress the potential explosion of the solution for appropriate moreover for sufficiently large q this stochastic functional system is exponentially stable these results can be used to examine stochastic stabilization

ito type stochastic fuzzy differential equations with delay abstract in the paper we give some foundations for the studies of stochastic fuzzy delayed differential equations we prove the existence and uniqueness of solutions to such the equations to obtain our result we assume that the coefficients of the equation satisfy the lipschitz condition together with linear growth condition we estimate the distance between approximate solution and exact solution also the stability of solution with respect to the initial history is shown an application of stochastic fuzzy delayed differential equations in the modeling of population growth is indicated

brief paper robustness of exponential stability of a class of stochastic functional differential equations with infinite delay we regard the stochastic functional differential equation with infinite delay dx t f x t dt g x t dw t as the result of the effects of stochastic perturbation to the deterministic functional differential equation email protected t f x t where x t x t q c 0 r n is defined by x t q x email protected email protected 0 we assume that the deterministic system with infinite delay is exponentially stable in this paper we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable

suppression and stabilisation of noise in this article we investigate the stochastic suppression and stabilisation of nonlinear systems given an unstable differential equation in which f satisfies the one sided polynomial growth condition we introduce two brownian noise feedbacks and therefore stochastically perturb this system into the nonlinear stochastic differential equation this article shows that appropriate may guarantee that this stochastic system exists as a unique global solution although the corresponding deterministic may explode in a finite time then sufficiently large q may ensure that this stochastic system is almost surely exponentially stable

almost sure and pth moment stability and stabilization of regime switching jump diffusion systems this work focuses on regime switching jump diffusions which include three classes of random processes brownian motions poisson processes and markov chains first a scalar linear system is treated as a benchmark model then stabilization of systems with one sided linear growth is considered next nonlinear systems that have a finite explosion time are treated in which regularization explosion suppression and stabilization are achieved by introducing appropriate diffusions together with poisson and markov chain perturbations this work reveals the impact of various random effects on the underlying systems for almost sure and p th moment stability and provides insight on stability and stabilization of switching jump diffusion systems

comparing two proposed measures of cochlear mechanical filter bandwidth based on stimulus frequency otoacoustic emissions it has been hypothesized that the sharpness of the cochlear mechanical filter is related to two measures based on stimulus frequency otoacoustic emissions sfoaes the first is the group delay of the sfoae the second is the bandwidth of the sfoae two tone suppression isoinput tuning characteristic a corollary of this is that natural variability in cochlear mechanical bandwidth within a population would lead to a positive correlation between these two sfoae based measures of tuning within that population to test this prediction sfoae group delay and sfoae two tone suppression isoinput tuning characteristics were measured in a sample of 16 audiometrically normal subjects contrary to the prediction no statistically significant correlation was found between the two bandwidth measures cochlear model simulations were used to aid the interpretation of this result these suggested that a positive correlation between the two measures is expected but that it may well be too weak to detect with the given sample size due to the influence on the sfoae measures of random inhomogeneities in basilar membrane impedance

noise induced stabilization of the recurrent neural networks with mixed time varying delays and markovian switching parameters the stabilization of recurrent neural networks with mixed time varying delays and markovian switching parameters by noise is discussed first a new result is given for the existence of unique states of recurrent neural networks nns with mixed time varying delays and markovian switching parameters in the presence of noise without the need to satisfy the linear growth conditions required by general stochastic markovian switching systems next a delay dependent condition for stabilization of concerned recurrent nns is derived by applying the ltd formula the gronwall inequality the law of large numbers and the ergodic property of markovian chain the results show that there always exists an appropriate white noise such that any recurrent nns with mixed time varying delays and markovian switching parameters can be exponentially stabilized by noise if the delays are sufficiently small

human cochlear tuning estimates from stimulus frequency otoacoustic emissions two objective measures of human cochlear tuning using stimulus frequency otoacoustic emissions sfoae have been proposed one measure used sfoae phase gradient delay and the other two tone suppression 2ts tuning curves here it is hypothesized that the two measures lead to different frequency functions in the same listener two experiments were conducted in ten young adult normal hearing listeners in three frequency bands 1 2 khz 3 4 khz and 5 6 khz experiment 1 recorded sfoae latency as a function of stimulus frequency and experiment 2 recorded 2ts iso input tuning curves in both cases the output was converted into a sharpness of tuning factor based on the equivalent rectangular bandwidth in both experiments sharpness of tuning curves were shown to be frequency dependent yielding sharper relative tuning with increasing frequency only a weak frequency dependence of the sharpness of tuning curves was observed for experiment 2 consistent with objective and behavioural estimates from the literature most importantly the absolute difference between the two tuning estimates was very large and statistically significant it is argued that the 2ts estimates of cochlear tuning likely represents the underlying properties of the suppression mechanism and not necessarily cochlear tuning thus the phase gradient delay estimate is the most likely one to reflect cochlear tuning

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

stability analysis for a class of stochastic delay nonlinear systems driven by g brownian motion abstract this paper is devoted to study the p th moment exponential stability problem for a class of stochastic delay nonlinear systems sdnss driven by g brownian motion the delays considered in this paper are time varying delays i t 0 1 i 3 and they are not required to be differentiable different from the traditional methods we use a new approach stochastic delay feedback controls we firstly compare the sdns with the corresponding stochastic nonlinear system sns instead of studying the stability of the sdns directly then we impose the condition on the sns to ensure the p th moment exponential stability of the sns furthermore we show that there is a positive constant such that the sdns is also p th moment exponentially stable provided in particular we give an implicit lower bound for which can be computed numerically

almost sure exponential stability of hybrid stochastic functional differential equations abstract this paper is concerned with the almost sure exponential stability of the n dimensional nonlinear hybrid stochastic functional differential equation sfde d x t f 1 x t t r t t d t g 2 x t t r t t d b t where x t x t u u 0 is a c 0 r n valued process b t is an m dimensional brownian motion while r t is a markov chain we show that if the corresponding hybrid stochastic differential equation sde d y t f y t r t t d t g y t r t t d b t is almost surely exponentially stable then there exists a positive number such that the sfde is also almost surely exponentially stable as long as we also describe a method to determine which can be computed numerically in practice

stabilisation of difference equations with noisy prediction based control abstract we consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction based control these perturbations may be multiplicative x n 1 f x n l n 1 f x n x n n 0 1 if they arise from stochastic variation of the control parameter or additive x n 1 f x n f x n x n l n 1 n 0 1 if they reflect the presence of systemic noise we begin by relaxing the control parameter in the deterministic equation and deriving a range of values for the parameter over which all solutions eventually enter an invariant interval then by allowing the variation to be stochastic we derive sufficient conditions less restrictive than known ones for the unperturbed equation under which the positive equilibrium will be globally a s asymptotically stable i e the presence of noise improves the known effectiveness of prediction based control finally we show that systemic noise has a blurring effect on the positive equilibrium which can be made arbitrarily small by controlling the noise intensity numerical examples illustrate our results

noise suppresses or expresses exponential growth in this paper we will show that noise can make a given system whose solutions grow exponentially become a new system whose solutions will grow at most polynomially on the other hand we will also show that noise can make a given system whose solutions are bounded become a new system whose solutions will grow exponentially in other words we reveal that the noise can suppress or expresses exponential growth

almost sure exponential stabilization by discrete time stochastic feedback control given an unstable linear scalar differential equation dot x t alpha x t alpha 0 we will show that the discrete time stochastic feedback control sigma x t tau tau db t can stabilize it that is we will show that the stochastically controlled system dx t alpha x t dt sigma x t tau tau db t is almost surely exponentially stable when sigma 2 2 alpha and tau 0 is sufficiently small where b t is a brownian motion and t tau is the integer part of t tau we will also discuss the nonlinear stabilization problem by a discrete time stochastic feedback control the reason why we consider the discrete time stochastic feedback control is because that the state of the given system is in fact observed only at discrete times say 0 tau 2 tau ldots for example where tau 0 is the duration between two consecutive observations accordingly the stochastic feedback control should be designed based on these discrete time observations namely the stochastic feedback control should be of the form sigma x t tau tau db t from the point of control cost it is cheaper if one only needs to observe the state less frequently it is therefore useful to give a bound on tau from below as larger as better

combining probability distributions from dependent information sources inferences or decisions in the face of uncertainty should be based on all available information thus when probability distributions for an uncertain quantity are obtained from experts models or

noise suppresses exponential growth under regime switching consider a given system under regime switching whose solution grows exponentially and suppose that the system is subject to environmental noise in some regimes can the regime switching and the environmental noise work together to make the system change significantly the answer is yes in this paper we will show that the regime switching and the environmental noise will make the original system whose solution grows exponentially become a new system whose solutions will grow at most polynomially in other words we reveal that the regime switching and the environmental noise will suppress the exponential growth

condition of vibrational stabilizability for a class of nonlinear systems a notion of vibrational stabilizability for a class of nonlinear systems is introduced and analyzed

stabilization of linear systems by noise it is proved that the biggest lyapunov number lambda max of the system dot x a f t x where a is a fixed d times d matrix and f t is a zero mean strictly stationary matrix valued stochastic process satisfies 1 d trace a leqq lambda max on the other hand for each varepsilon 0 there is a process f t for which lambda max leqq 1 d trace a varepsilon in particular the system dot x ax can be stabilized by zero mean stationary parameter noise if and only if trace a 0 the stabilization can be accomplished by a one dimensional noise source the results carry over to the case where a is a stationary process they are also true for f t white noise

stochastic stabilization and destabilization it is shown in this paper that any nonlinear systems dot x t f x t t in rd can be stabilized by brownian motion provided f hook x t k x for some k 0 on the other hand this system can also be destabilized by brownian motion if the dimension d 2 similar results are also obtained for any given stochastic differential equation dx t f hook x t t g x t t dw t

mean square exponential stability of stochastic nonlinear delay systems abstractin this paper we are concerned with the stability of stochastic nonlinear delay systems different from the previous literature we aim to show that when the determinate nonlinear delay system is globally exponentially stable the corresponding stochastic nonlinear delay system can be mean square globally exponentially stable in particular we remove the linear growth condition and introduce a new polynomial growth condition for g x t x t t which overcomes the limitation of application scope and the boundedness of diffusion term form finally we provide an example to illustrate our results

modeling expert judgments for bayesian updating this paper examines how a bayesian decision maker would update his her probability p for the occurrence of an event a in the light of a number of expert opinions expressed as probabilities q 1 cdots q n of a it is seen among other things that the linear opinion pool lambda 0p sum n i 1 lambda iq i corresponds to an application of bayes theorem when the decision maker has specified only the mean of the marginal distribution for q 1 cdots q n and requires his her formula for the posterior probability of a to satisfy a certain consistency condition a product formula similar to that of bordley 1982 is also derived in the case where the experts are deemed to be conditionally independent given a and given its complement

noise suppresses explosive solutions of differential systems a new general polynomial growth condition abstract recently liu and shen 2012 have discussed the problem of suppression explosive solutions by noise for nonlinear deterministic differential system with coefficients satisfying a general one sided polynomial growth condition liu and shen introduced the brownian noise feedback x t x t d b t to the nonlinear differential system and they showed that the corresponding stochastic system has a unique global solution however liu and shen s condition is still very restrictive and many more general nonlinear differential systems fail this paper aims to introduce a new more general polynomial growth condition which can be applied to more nonlinear differential systems under the new polynomial growth condition we show that the considered stochastic system has a unique global solution although the corresponding deterministic system may explode in a finite time moreover we show that the flexible stochastic feedback g x t can guarantee the solution not only be limited in the sense of moment but also grows at most polynomially finally we provide two examples to illustrate superiority of the new general polynomial growth condition

a new type of stability theorem for stochastic systems with application to stochastic stabilization in this note a new type of stability theorem for stochastic systems is established firstly based on this stability theorem and its corollaries stochastic stabilization and destabilization by noise are further investigated in the note the local lipschitz condition is weakened to the generalized local lipschitz condition the commonly used linear growth condition or one side linear growth condition is weakened to the generalized one side linear growth condition which is local variable and nonlinear admits nearly arbitrary variability in the time and real nonlinearity in the state as an application a simple and direct design method is proposed for finding a noise strength hat mathbb g t x so that the added noise hat mathbb g t x d hat b t stabilizes an unstable stochastic system or destabilizes a stable one a numerical example is presented at the end of the note to illustrate the usage and efficiency of the proposed design method of the note

stochastic stabilisation of functional differential equations in this paper we investigate the problem of stochastic stabilisation for a general nonlinear functional differential equation given an unstable functional differential equation dx t dt f t xt we stochastically perturb it into a stochastic functional differential equation dx t f t xt dt x t db t where is a matrix and b t a brownian motion while xt x t 0 under the condition that f satisfies the local lipschitz condition and obeys the one side linear bound we show that if the time lag is sufficiently small there are many matrices for which the stochastic functional differential equation is almost surely exponentially stable while the corresponding functional differential equation dx t dt f t xt may be unstable

stochastic differential delay equation moment stability and application to hematopoietic stem cell regulation system we study the moment stability of the trivial solution of a linear differential delay equation in the presence of additive and multiplicative white noise the results established here are applied to examining the local stability of the hematopoietic stem cell hsc regulation system in the presence of noise the stability of the first moment for the solutions of a linear differential delay equation under stochastic perturbation is identical to that of the unperturbed system however the stability of the second moment is altered by the perturbation we obtain using laplace transform techniques necessary and sufficient conditions for the second moment to be bounded in applying the results to the hsc system we find that the system stability is sensitive to perturbations in the stem cell differentiation and death rates but insensitive to perturbations in the proliferation rate

brief paper noise suppresses explosive solutions of differential systems with coefficients satisfying the polynomial growth condition in this paper we investigate the problem of suppression explosive solutions by noise for nonlinear deterministic differential system given a deterministic differential system email protected t f y t t with coefficients satisfying a more general one sided polynomial growth condition we introduce brownian noise feedback and therefore stochastically perturb this system into the nonlinear stochastic differential system dx t f x t t dt x t email protected t db t we show that appropriate b s guarantee that this stochastic system exists as a unique global solution although the corresponding deterministic systems may explode in a finite time under some weaker conditions we reveal that the single noise x t email protected t db t can also make almost every path of the solution of corresponding stochastically perturbed system grow at most polynomially

global stochastic stability analysis for stochastic neural networks with infinite delay and markovian switching we consider a novel stochastic nns model the method is the lyapunov method stochastic analysis technique and m matrix theory we derive sufficient criteria for three kinds of stochastic stability numerical examples demonstrate the applicability and effectiveness of the theoretical theorems this paper focuses on the stochastic stability for a novel kind of stochastic neural networks with infinite delay and markovian switching by using the lyapunov method stochastic analysis technique and m matrix theory some simple and easily testable sufficient conditions are presented to ensure the trivial solution is stochastically stable stochastically asymptotically stable and globally stochastically asymptotically stable respectively as a subsequent result we develop the conditions that guarantee global stochastic asymptotic stability for stochastic neural networks with infinite delay as well as global asymptotic stability for neural networks with infinite delay from the perspective of theory the derived stability criteria include some existing ones as its special cases and are thus less conservative finally two examples are given to demonstrate the applicability and effectiveness of the theoretical theorems

stabilization and destabilization of nonlinear differential equations by noise this paper considers the stabilization and destabilization by a brownian noise perturbation that preserves the equilibrium of the ordinary differential equation x t f x t in an extension of earlier work we lift the restriction that f obeys a global linear bound and show that when f is locally lipschitz a function g can always be found so that the noise perturbation g x t db t either stabilizes an unstable equilibrium or destabilizes a stable equilibrium when the equilibrium of the deterministic equation is nonhyperbolic we show that a nonhyperbolic perturbation suffices to change the stability properties of the solution

brief paper almost sure exponential stabilisation of stochastic systems by state feedback control so far a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability this paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean square sense the results are expressed in terms of linear matrix inequalities lmis which are easy to be checked in practice by using matlab toolbox moreover the control structure in this paper appears not only in the drift part but also in the diffusion part of the underlying stochastic system

noise expresses exponential growth under regime switching consider a given system under regime switching whose solution grows at most polynomially and suppose that the system is subject to environmental noise in some regimes can regime switching and the environmental noise work together to make the system change significantly the answer is yes in this paper we will show that the regime switching and the environmental noise will make the original system whose solution grows at most polynomially become a new system whose solution will grow exponentially in other words we reveal that regime switching and the environmental noise will express the exponential growth

the asymptotic properties of the suppressed functional differential system by brownian noise under regime switching abstractin the previous work by wu et al it was shown that the polynomial brownian noise may suppress the potential explosion of the nonlinear system without the linear growth condition or the one sided linear growth condition and the linear brownian noise may stabilise this suppressed system this paper is a continuation of our previous article and considers the asymptotic properties of the suppressed functional differential system under regime switching these asymptotic properties show that the suppressed functional differential system by polynomial brownian noise will grow with at most polynomial speed

identification of otoacoustic emissions components by means of adaptive approximations clicks and a set of tone bursts covering the same frequency band were applied as a stimuli evoking otoacoustic emissions oae recorded otoacoustic emissions were decomposed into the basic waveforms by means of high resolution adaptive time frequency approximation method based on the matching pursuit algorithm the method allows for description of the signal components in terms of frequencies time occurrences time spans and energy the analysis of oae s energy density distributions in time frequency space revealed that click responses can be considered as linear superpositions of responses to tone bursts the frequency latency relationship was studied and compared with earlier works the method made possible the exhaustive description of the resonant modes specific for given subject ear they were characterized not only by the close frequencies appearing for different tones but they usually had similar latencies and time spans short time and long time resonant modes were identified the second ones

the asymptotic properties of the suppressed system by brownian noise in the previous work by the second author it was shown that the polynomial brownian noise may suppress the potential explosion of the nonlinear system without the linear growth condition or the one sided linear growth condition and the linear brownian noise may stabilise this suppressed system this article is a continuation of our previous paper and considers the asymptotic properties of the suppressed system these asymptotic properties show that the suppressed system by polynomial brownian noise will grow with at most polynomial speed