stochastic stabilization and destabilization of nonlinear differential equations abstract this paper is concerned with the stochastic stabilization and destabilization of nonlinear differential equations which more precisely further develops the general theory of stochastic stabilization and destabilization that was studied by mao 1994 4 and appleby et al 2008 1 the proposed results are of substantial improvements and reveal the more fundamental principle for stochastic stabilization and destabilization of dynamical systems which is also verified with examples of application to mass action systems

statistical and stabilizability properties of equivalent discrete time systems with stochastic parameters this paper considers the influence of the statistics of a scalar continuous time system with white stochastic parameters on the statistics the correlation and the stabilizability of the corresponding scalar equivalent discrete time system by means of numerical examples some insight into the behaviour of the equivalent discrete time system is given furthermore these examples illustrate the crucial influence of the correlation between the state and control dependent noise of the continuous time system on the stabilizability of the equivalent discrete time system

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

stabilization of a plane periodic channel flow by noise wall normal controllers the steady state flows in a 2 d channel with periodic conditions along the axis are stabilized by a boundary feedback stochastic controller with vertical velocity observation which acts on the normal component of velocity only

lyapunov exponents and rotation number of two dimensional systems with telegraphic noise exact expressions for the exponential growth rates lyapunov exponents and rotation numbers of two dimensional systems perturbed by telegraphic noise are derived asymptotic expansions for small large slow and fast noise and the white noise limit are constructed then results are applied to the random oscillator stochastic stability in particular stabilization by noise and stochastic bifurcation

a comodule bialgebra structure for word series substitution and mould composition abstract an internal coproduct is described which is compatible with hoffman s quasi shuffle product hoffman s quasi shuffle hopf algebra with deconcatenation coproduct is a comodule hopf algebra over the bialgebra thus defined the relation with ecalle s mould calculus i e mould composition and contracting arborification is precised

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

on the stabilization of the homogeneous bilinear systems abstract the problem of stabilizing the single input homogeneous bilinear systems is considered a special class of these systems is considered the matrix of the linear i e control independent term of the right hand side is semitable while the matrix of the bilinear term is skew symmetric two types of stabilization are investigated constant feedback global asymptotic stabilization and practical stabilization by a family of the linear feedbacks it will be shown for the planar case that the above system is always practically stabilizable by a family of the linear feedbacks for n 3 the solution of both stabilization problems depends on the mutual position of the expanding direction of the linear part and the direction of the infinitesimal rotation defined by the bilinear term

a harmonic framework for controllability in linear continuous time periodic systems controllability of linear continuous time periodic systems is dealt with via a harmonic analysis approach for the first time in this paper this approach reveals that controllability of continuous time periodic systems can be connected to necessary and sufficient conditions expressed explicitly with fourier coefficients of the system matrices which can be interpreted in a way similar to what we have seen in linear time invariant cases these controllability conditions shed new light upon structural characteristics of continuous time periodic systems that are hard to know by means of existing time domain controllability criteria in the literature controllability canonical decomposition of linear continuous time periodic systems is revisited through state coordinate transforms of strong analytic features the results are heuristic and significant for examining structural characteristics of continuous time periodic systems and extending controllability related techniques that are widely employed in linear time invariant systems to linear continuous time periodic systems

relaxing the conditions for parameter estimation based observers of nonlinear systems via signal injection parameter estimation based observers are a new kind of state reconstruction methods where the state observation task is translated into an on line parameter estimation problem a key step for its application is the transformation of the system dynamics into a particular cascade form which involves the solution of a partial differential equation that moreover should satisfy some injective requirement in this note we use a recently proposed technique of signal injection to generate new outputs and simplify these tasks in this way we make this observer applicable to a wider class of nonlinear systems even with indistinguishable states the application of the proposed approach is illustrated with the design of a novel sensorless controller for magnetic levitation systems

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

planarly branched rough paths and rough differential equations on homogeneous spaces abstract this work studies rough differential equations rdes on homogeneous spaces we provide an explicit expansion of the solution at each point of the real line using decorated planar forests the notion of planarly branched rough path is developed following gubinelli s branched rough paths the main difference being the replacement of the butcher connes kreimer hopf algebra of non planar rooted trees by the munthe kaas wright hopf algebra of planar rooted forests the latter underlies the extension of butcher s b series to lie butcher series known in lie group integration theory planarly branched rough paths admit the study of rdes on homogeneous spaces the same way gubinelli s branched rough paths are used for rdes on finite dimensional vector spaces an analogue of lyons extension theorem is proven under analyticity assumptions on the coefficients and when the holder index of the driving path is one we show convergence of the planar forest expansion in a small time interval

correlation free forms for nonlinear stochastic systems abstract an asymptotic method for analysis of nonlinear systems with wide band and high frequency stochastic perturbation is developed correlation free ito limiting equations are derived and a generalization of the wong zakai correction for the drift term is obtained a correction for the diffusion term is also shown to exist several illustrative examples are considered

stabilisation of hybrid stochastic systems with levy noise by discrete time feedback control this paper is devoted to deal with the stabilisation problems of continuous time hybrid stochastic systems often described by stochastic differential equations with markovian switching with levy

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

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

pole placement capabilities of vibrational control vibrational control modifies the system dynamics by introducing fast zero average parametric oscillations however this property is constrained by the trace invariance condition which limits the pole placement capabilities this paper provides the necessary and sufficient conditions under which pole assignment by vibrational control in certain parts of the complex plane is possible

brief paper exponential stabilization of the linearized navier stokes equation by pointwise feedback noise controllers we address the problem of exponential stabilization in probability of the linearized navier stokes equations in an equilibrium point this is done by designing a linear stochastic feedback controller with support in a point or on a discrete set of points of the domain this controller consists of a steady state impulse component with support in a finite set of points modulated by an unsteady feedback noise controller

lyapunov exponents of hybrid stochastic heat equations in this paper we investigate a class of hybrid stochastic heat equations by explicit formulae of solutions we not only reveal the sample lyapunov exponents but also discuss the pth moment lyapnov exponents moreover several examples are established to demonstrate that unstable deterministic or stochastic dynamical systems can be stabilized by markovian switching

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

controlling rough paths abstract we formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints this allows us to define a good notion of integral with respect to irregular paths with holder exponent greater than 1 3 e g samples of brownian motion and study the problem of the existence uniqueness and continuity of solution of differential equations driven by such paths we recover young s theory of integration and the main results of lyons theory of rough paths in holder topology

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

dynamics and absorption properties of stochastic equations with holder diffusion coefficients abstract in this article we characterize the dynamics and absorption properties of a class of stochastic differential equations around singular points where both the drift and diffusion functions vanish according to the holder coefficient of the diffusion function around the singular point we identify different regimes a regime where the solutions almost surely reach the singular point in finite time and regimes of exponential attraction or repulsion from the singular point stability of the absorbing state large deviations for the absorption time existence of stationary or quasi stationary distributions are discussed in particular we show that quasi stationary distributions only exist for 3 4 and for 3 4 1 no quasi stationary distribution is found and numerical simulations tend to show that the process conditioned on not being absorbed initiates an almost sure exponential convergence towards the absorbing state as is demonstrated to be true for 1 these results have several implications in the understanding of stochastic bifurcations and we completely unfold two generic situations the pitchfork and saddle node bifurcations and discuss the hopf bifurcation in the appendix

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

an assessment of the direction finding accuracy of bat biosonar beampatterns in the biosonar systems of bats emitted acoustic energy and receiver sensitivity are distributed over direction and frequency through beampattern functions that have diverse and often complicated geometries this complexity could be used by the animals to determine the direction of incoming sounds based on spectral signatures the present study has investigated how well bat biosonar beampatterns are suited for direction finding using a measure of the smallest estimator variance that is possible for a given direction cramer rao lower bound crlb crlb values were estimated for numerical beampattern estimates derived from 330 individual shape samples 157 noseleaves used for emission and 173 outer ears pinnae at an assumed 60 db signal to noise ratio the average value of the crlb was 3 9 which is similar to previous behavioral findings distribution for the crlbs in individual beampatterns had a positive skew indicating the existence of regions where a given beampattern does not support a high accuracy the highest supported accuracies were for direction finding in elevation with the exception of phyllostomid emission patterns no large obvious differences in the crlb greater 2 in the mean were found between the investigated major taxonomic groups suggesting that different bat species have access to similar direction finding information

characterization of the diversity in bat biosonar beampatterns with spherical harmonics power spectra the biosonar beampatterns found across different bat species are highly diverse in terms of global and local shape properties such as overall beamwidth or the presence location and shape of multiple lobes it may be hypothesized that some of this variability reflects evolutionary adaptation to investigate this hypothesis the present work has searched for patterns in the variability across a set of 283 numerical predictions of emission and reception beampatterns from 88 bat species belonging to four major families rhinolophidae hipposideridae phyllostomidae vespertilionidae this was done using a lossy compression of the beampatterns that utilized real spherical harmonics as basis functions the resulting vector representations showed differences between the families as well as between emission and reception these differences existed in the means of the power spectra as well as in their distribution the distributions were characterized in a low dimensional space found through principal component

stabilization by noise for a class of stochastic reaction diffusion equations we prove uniqueness ergodicity and strongly mixing property of the invariant measure for a class of stochastic reaction diffusion equations with multiplicative noise in which the diffusion term in front of the noise may vanish and the deterministic part of the equation is not necessary asymptotically stable to this purpose we show that the l1 norm of the difference of two solutions starting from any two different initial data converges a s to zero as time goes to infinity

the equivalent discrete time optimal control problem for continuous time systems with stochastic parameters this paper considers the transformation of the digital optimal control problem to an equivalent discrete time optimal control problem for linear continuous time systems with continuous time white stochastic parameters and additive continuous time white noise the observations available at the sampling instants are in general non linear and corrupted by discrete time noise the equivalent discrete time system has white stochastic parameters expressions are derived for the first and second moments of these parameters and for the cost criterion parameters which are explicit in the parameters and the statistics of the continuous time system

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

ramification of rough paths the stack of iterated integrals of a path is embedded in a larger algebraic structure where iterated integrals are indexed by decorated rooted trees and where an extended chen s multiplicative property involves the durr connes kreimer coproduct on rooted trees this turns out to be the natural setting for a non geometric theory of rough paths

regularization and stabilization of randomly switching dynamic systems this work concerns regularization or explosion suppression and stabilization of randomly switching dynamic systems by selecting suitable input functions starting with a randomly switching system modulated by a continuous time markov chain our aim is to find a feedback control input function so that the system becomes stable but before addressing the stabilization issue another problem needs to be resolved first because of the fast growth in the continuous state variable the solution of the system has a finite explosion time with probability one to ensure the existence of global solutions a feedback control a noise perturbation is added to make the system regular then another feedback control a second perturbing noise is added to ensure the stability of the resulting systems owing to the nonlinearity closed form solutions are often virtually impossible to obtain thus a discrete time approximation algorithm is constructed under simple conditions a suitably interpolated sequence of the

stabilisation of linear pdes by stratonovich noise some results concerning the stability and stabilisation of stochastic linear partial differential equations in the sense of stratonovich are proved the main result ensures that a deterministic linear pde can be stabilised by adding a suitable stratonovich noise if and only if the linear partial differential operator has negative trace

a stability study of a new explicit numerical scheme for a system of differential equations with a large skew symmetric component explicit numerical methods for the solution of a system of stiff differential equations suffer from a time step size that approaches zero in order to satisfy stability conditions implicit schemes allow a larger time step but require more computations when the differential equations are dominated by a skew symmetric component the problem is not stiffness in the sense that the size of the eigenvalues are unequal rather that the real eigenvalues are dominated by imaginary eigenvalues a skew dominated system of this type may be seen in magnetohydrodynamics and in control problems we present and compare analytical results for stable time step limits for several explicit methods including the super time stepping method of alexiades amiez and gremaud which is an explicit runge kutta method for parabolic partial differential equations and a new method modeled on a predictor corrector scheme with multiplicative operator splitting this new explicit method presented in regular and super time stepping form increases stability without forcing the step size to zero

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 stabilization of differential systems with general decay rate some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general decay rate are first proved then these results are interpreted as suitable stabilization ones for deterministic and stochastic systems also they permit us to construct appropriate linear stabilizers in some particular situations

stabilization of linear systems by rotation we introduce the concept of stabilization by rotation for deterministic linear systems with negative trace this concept encompasses the well known concept of vibrational stabilization introduced by meerkov in the 1970s and is a deterministic version of stabilization by noise for stochastic systems as introduced by arnold and coworkers in the 1980s it is shown that a linear system with negative trace can be stabilized by adding a skew symmetric matrix multiplied by a suitable scalar so called gain function possibly a constant which is su ciently large to overcome the problem of what is su ciently large we also present a servo mechanism which which tunes the gain function by learning from the trajectory until flnally the trajectory tends to zero this approach allows to show that one of meerkov s assumptions for vibrational stabilization is super uous moreover while meerkov as well as arnold and coworkers assume that a stabilizing periodic function or the noise has su ciently large frequency and amplitude we also provide a servo mechanism to determine this function dynamically in a deterministic setup

chaos noise and synchronization reconsidered in a recent paper maritan and banavar phys rev lett 72 1451 1994 reported the synchronization of identical chaotic systems by additive noise we relate such a synchronization to the maximum lyapunov exponent of a single system and discuss the underlying mechanisms of the effect in the case of the lorenz equations the nonvanishing mean of the noise mimics a parameter change leading to synchronization for the logistic map a state dependence of the fluctuations is induced by the boundary conditions

convergence of lie group integrators we relate two notions of local error for integration schemes on riemannian homogeneous spaces and show how to derive global error estimates from such local bounds in doing so we prove for the first time that the lie butcher theory of lie group integrators leads to global error estimates

global asymptotic stabilization of nonlinear deterministic systems using wiener processes the objective of this study is to present a noise assisted stabilization method and a constructive method for designing a stabilizing controller we investigate the stabilization of a deterministic nonlinear affine system by using a controller with a wiener process our approach focuses on the global asymptotic stabilization of nonholonomic systems the proposed method for designing a stabilizing controller is based on the notion of a stochastic control lyapunov function we show that if there exists a stochastic control lyapunov function with small control property the designed controller globally asymptotically stabilizes a given system with probability one

synchronization by noise we provide sufficient conditions for synchronization by noise i e under these conditions we prove that weak random attractors for random dynamical systems consist of single random points in the case of sde with additive noise these conditions are also essentially necessary in addition we provide sufficient conditions for the existence of a minimal weak point random attractor consisting of a single random point as a result synchronization by noise is proven for a large class of sde with additive noise in particular we prove that the random attractor for an sde with drift given by a multidimensional double well potential and additive noise consists of a single random point all examples treated in tearne probab theory relat fields 141 1 2 1 18 2008 are also included

turbulence effects on fluidelastic instability of a cylinder in a shear flow abstract fluidelastic instability is the main mechanism that causes severe damages in flow induced vibration experiments show that grid generated turbulence can affect the stability of the system which is modeled as an ornstein uhlenbeck process the dynamic stability of a four dimensional system under real noise excitation is studied through the determination of the p th moment lyapunov exponent and the lyapunov exponent the partial differential eigenvalue equation governing the moment lyapunov exponent is established for small noise amplitudes a method of regular perturbation is used to determine analytical expansions of the moment lyapunov exponents and lyapunov exponents which are shown to be in good agreement with those obtained using numerical approaches the analytical method is applied to study the stability of a cylinder in a shear flow where fluidelastic instability is known to occur the results demonstrate that the unstable system can be stabilized under certain conditions and the effect of stabilization is proportional to the turbulence intensity which agrees with experimental observations

the geometry of the space of branched rough paths we construct an explicit transitive free action of a banach space of holder functions on the space of branched rough paths which yields in particular a bijection between theses two spaces this endows the space of branched rough paths the structure of a principal homogeneous space over a banach space and allows to characterize its automorphisms the construction is based on the baker campbell hausdorff formula and on the hairer kelly map which allows to describe branched rough paths in terms of anisotropic geometric rough paths

a stochastic model for the evolution of bone metastasis persistence and recovery abstract bone metastasis is a complex disease that modifies the natural dynamics of the bone remodeling process which is vital for maintaining a healthy bone structure nowadays there are deterministic differential models that describe the bone metastasis evolution by considering interaction mechanisms between cancer cells and basic bone cells such as osteoclasts and osteoblasts based on these deterministic models a stochastic differential model is proposed to describe the bone metastasis evolution in order to analyze the effect of environmental fluctuations inclusions conditions for the existence and uniqueness of a nonnegative solution of the proposed stochastic model are given to characterize whether the invasion of cancer persists or is eradicated finally we illustrate different dynamical behaviors of the stochastic solution by means of numerical simulations

hopf algebras renormalization and noncommutative geometry we explore the relation between the hopf algebra associated to the renormalization of qft and the hopf algebra associated to the ncg computations of tranverse index theory for foliations

eigenbeam analysis of the diversity in bat biosonar beampatterns a quantitative analysis of the interspecific variability in the biosonar beampatterns of bats has been performed on a data set that consisted of 267 emission and reception beampatterns from 98 different species the beampatterns were aligned using a pairwise optimization framework defined by a rotation for which a cost function is minimized the cost function was defined by a p norm computed over all direction and summed across a discrete set of evenly sampled frequencies for a representative subset of beampatterns it was found that all pairwise alignments between beampatterns result in a global minimum that fell near the plane bisecting the mean direction of each beampattern and containing the origin following alignment the average beampattern was found to consist of a single lobe that narrowed with increasing frequency variability around the average beampattern was analyzed using principle component analysis pca that resulted in eigenbeams the first three eigenbeams were found to control the beamwidth of the beampattern across frequency while higher rank eigenbeams accounted for symmetry breaks and changes in lobe direction reception and emission beampattern could be differentiated based on their pca scores using only a small number of eigenbeams

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

regularization by noise for stochastic hamilton jacobi equations we study regularizing effects of nonlinear stochastic perturbations for fully nonlinear pde more precisely path by path l infty bounds for the second derivative of solutions to such pde are shown these bounds are expressed as solutions to reflected sde and are shown to be optimal

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

post symmetric braces and integration of post lie algebras abstract the aim of this letter is twofold firstly we introduce the post lie analogue of the notion of a symmetric brace algebra termed in the sequel post symmetric brace algebra these brace algebras are defined using a suitable algebraic operad which turns out to be isomorphic to the operad of the post lie algebras secondly using these new brace algebras together with the so called post lie magnus expansion we aim both to analyze the enveloping algebra of the corresponding post lie algebra and to compare the two baker campbell hausdorff series there naturally defined

a numerical study of the role of the tragus in the big brown bat a comprehensive characterization of the spatial sensitivity of an outer ear from a big brown bat eptesicus fuscus has been obtained using numerical methods and visualization techniques pinna shape information was acquired through x ray microtomography it was used to set up a finite element model of diffraction from which directivities were predicted by virtue of forward wave field projections based on a kirchhoff integral formulation digital shape manipulation was used to study the role of the tragus in detailed numerical experiments the relative position between tragus and pinna aperture was found to control the strength of an extensive asymmetric sidelobe which points in a frequency dependent direction an upright tragus position resulted in the strongest sidelobe sensitivity using a bootstrap validation paradigm the results were found to be robust against small perturbations of the finite element mesh boundaries furthermore it was established that a major aspect of the tragus effect position dependence can be studied in a simple shape model an obliquely truncated horn augmented by a flap representing the tragus in the simulated wave field around the outer ear structure strong correlates of the tragus rotation were identified which provide a direct link to the underlying physical mechanism

internal stabilization of the oseen stokes equations by stratonovich noise abstract the design of a stratonovich noise feedback controller with support in an arbitrary open subset o 0 of o is described this exponentially stabilizes in probability that is with probability one the oseen stokes systems in a domain o r d d 2 3 this completes the stabilization results from the author s work barbu 2011 3 which is concerned with design of an ito noise stabilizing controller

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

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

convergence rate determined for gradient based adaptive estimators abstract a convergence rate estimate is derived for the homogeneous gradient based adaptive linear estimator algorithm this estimate involves the eigenvalues of the regression vector covariance matrix yielding a useful measure for the choice of input signals for adaptive parameter estimation the connection between this criterion and those more familiar from nonadaptive system identification is made and comparisons are drawn between the two areas