finitely many delta interactions with supports on concentric spheres using the theory of self adjoint extensions of symmetric operators the precise mathematical definition of the quantum hamiltonian describing a finite number of interactions with supports on concentric spheres is given its resolvent is also derived its spectral properties are described and it is shown how this hamiltonian can be obtained as a norm resolvent limit of a family of local scaled short range hamiltonians

the general properties of discrete time competitive dynamical systems abstract for strongly competitive discrete time dynamical systems on a strongly ordered topological vector space it is proved that any or limit set is unordered and lies on some invariant hypersurface with codimension one which generalizes hirsch s results for competitive autonomous systems of ordinary differential equations to competitive maps in a very general framework and implies the sarkovskii s theorem for planar strongly competitive and monotone maps we also show that the definition of competitiveness gives more restriction on homeomorphic property

regular dynamics in a delayed network of two neurons with all or none activation functions we consider a delayed network of two neurons with both self feedback and interaction described by an all or none threshold function the model describes a combination of analog and digital signal processing in the network and takes the form of a system of delay differential equations with discontinuous nonlinearity we show that the dynamics of the network can be understood in terms of the iteration of a one dimensional map and we obtain simple criteria for the convergence of solutions the existence multiplicity and attractivity of periodic solutions

the hamiltonian of the harmonic oscillator with an attractive delta prime interaction centred at the origin as approximated by the one with a triple of attractive delta interactions in this note we provide an alternative way of defining the self adjoint hamiltonian of the harmonic oscillator perturbed by an attractive delta interaction of strength beta centred at 0 the bottom of the confining parabolic potential that was rigorously defined in a previous paper by means of a coupling constant renormalisation here we get the hamiltonian as a norm resolvent limit of the harmonic oscillator hamiltonian perturbed by a triple of attractive delta interactions thus extending the cheon shigehara approximation to the case in which a confining harmonic potential is present

critical points for a one dimensional schrodinger operator with finite number of point delta interactions and number of eigenvalues for a one dimensional schrodinger operator with finite number n of point delta interactions the parameters are the n intensities n 1 intercenter distances and the mass a point pc in parameter space is a critical point if a continuous path p t with p 0 pc can be found such as one eigenvalue of the hamiltonian tends to zero when t tends to zero the number of eigenvalues changes only at a critical point the critical points are determined as the roots of the determinant of an n 1 order real symmetric tridiagonal matrix whose entries are simple functions of the parameters a simple algorithm is given for the determination of the number of eigenvalues from the parameters in the general case for the two particular cases namely equidistant centers and equal intensity parameters for the first case and equidistant centers and alternating intensity parameters for the second case the critical points and number of eigenvalues are determined analytically

convergence to equilibria in scalar nonquasimonotone functional differential equations abstract we consider a class of scalar functional differential equations generating a strongly order preserving semiflow with respect to the exponential ordering introduced by smith and thieme it is shown that the boundedness of all solutions and the stability properties of an equilibrium are exactly the same as for the ordinary differential equation which is obtained by ignoring the delays the result on the boundedness of the solutions combined with a convergence theorem due to smith and thieme leads to explicit necessary and sufficient conditions for the convergence of all solutions starting from a dense subset of initial data under stronger conditions guaranteeing that the functional differential equation is asymptotically equivalent to a scalar ordinary differential equation a similar result is proved for the convergence of all solutions

interval estimation for lpv systems applying high order sliding mode techniques in this paper the problem of design of interval observers for linear parameter varying lpv systems containing non detectable or non strongly observable parts is addressed firstly a high order sliding mode hosm method is applied to the strongly observable subsystem obtained by an appropriate change of coordinates to estimate the state and its derivative secondly this information is used to decrease the level of uncertainty in the rest of the system which leads to improvement of accuracy of the set membership estimates generated by an interval observer moreover it is shown that hosm techniques allows us to relax the applicability conditions of standard interval observer design methods the efficiency of the proposed approach is demonstrated through simulation examples

a model for the growth of a population exhibiting stage structure cannibalism and cooperation abstract a model of a stage structured population with fixed maturity time for the immature stage and interaction terms that may be interpreted as cooperation or cannibalism is proposed the existence and stability of the equilibrium set are discussed in the case of cannibalism it is shown by a numerical example how a hopf bifurcation could result in a stable periodic solution

asymptotic constancy for pseudo monotone dynamical systems on function spaces abstract a pseudo monotone dynamical system is a dynamical system which preserves the order relation between initial points and equilibrium points the purpose of this paper is to present some convergence oscillation and order stability criteria for pseudo monotone dynamical systems on function spaces for which each constant function is an equilibrium point some applications to neutral functional differential equations and semilinear parabolic partial differential equations with neumann boundary condition are given

on the convergence of linear switched systems this paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems we provide a collection of results that use weak dwell time dwell time strong dwell time permanent and persistent activation hypothesis the obtained results are shown to be tight by counterexample finally we apply our result to the three cell converter

strongly order preserving semiflows generated by functional differential equations the aim of this paper is to apply some recently developed improvements in the theory of monotone dynamical systems due to the authors 12 13 j to certain systems of functional differential equations fde s which do not enjoy the quasimonotone property considered by one of us in 9 the present work extends our previous results in this direction for scalar equations in 111 to systems in the fundamental paper s m w hirsch establishes that most orbits of a strongly monotone scmiflow on a strongly ordered space x tend to the set e of equilibria employing ideas of hirsch and of h matano 7 the authors have extended the theory to obtain some improvements in the results of hirsch and matano under matano s weaker assumption that the semiflow is strongly order preserving recently in 13 we gave sufficient conditions for most orbits of a strongly order preserving semiflow to converge to an equilibrium these conditions require additional smoothness of the semiflow and a certain strong monotonicity condition for the linearized flow determined by the variational equation about each equilibrium p policik s has also given sufficient conditions for most orbits to converge for semilinear parabolic evolution equations possessing certain strong monotonicity properties in this paper wc apply the convergence results developed in 131 to nonquasimonotone fde s in this introduction wc briefly review the application of monotone dynamical systems theory to fde s enjoying the quasimonotone property this research appeared in 9 133 then we state one of the main results of this paper which applies when the quasimonotone property fails but when another property m holds some simple examples are given which

stabilization for degenerate diffusion with absorption abstract the purpose of this paper is to study the limit in l 1 of solutions of general initial boundary value problems of the form ut w g x u and u w in a bounded domain with general boundary conditions of the form w w 0 where and are maximal monotone graphs and g r r is a nonincreasing continuous function in r r we prove that a solution stabilizes in l 1 as t to a function u l 1 which satisfies u x 1 c g x 1 0 a e x with c 1 0 so if for instance 1 0 1 0 g x 1 0 0 then a solution stabilizes by converging to 0 in l 1 as t

discrete order preserving semigroups and stability for periodic parabolic differential equations on etudie la stabilite globale des solutions des equations paraboliques dans une forme non auto adjointe avec des coefficients periodiques dans le temps la structure mathematique est celle des semigroupes preservant l ordre a temps discret s n n e n sur un reseau de banach

convergence to periodic solutions in periodic quasimonotone reaction diffusion systems abstract the author studies the periodic time dependent quasimonotone reaction diffusion systems u i t d i u i f i t x u 1 u n t 0 x u i n i u i 0 t 0 x u i x 0 u 0 i x x formula i 1 2 n in a proper banach space satisfying i fi uj 0 for all 1 i j n ii f t x u is periodic in t of period 0 and iii fi t x u fi t x u for all 0 1 and i 1 2 n it is proved that every solution of such a system converges to a periodic solution the same result also holds if we replace iii by iii f t x u is analytic and every periodic solution is liapounov stable

complicated dynamics of scalar reaction diffusion equations with a nonlocal term we consider the dynamics of scalar equations ut uxx f x u c x u 0 x l where denotes some weighted spatial average and dinchlet boundary conditions are assumed prescribing f c appropriately it is shown that complicated dynamics can occur specifically linearisations at equilibria can have any number of purely imaginary eigenvalues moreover the higher order terms of the reduced vector field in an associated centre manifold can be prescribed arbitrarily up to any finite order these results are in marked contrast with the case 0 where bounded solutions are known to converge to equilibrium

effects of a degeneracy in the competition model part i classical and generalized steady state solutions abstract we study the competition model where the coefficient functions are strictly positive over the underlying spatial region except b x which vanishes in a nontrivial subdomain of and is positive in the rest of we show that there exists a critical number such that if then the model behaves similarly to the well studied classical competition model where all the coefficient functions are positive constants but when new phenomena occur our results demonstrate the fact that heterogeneous environmental effects on population models are not only quantitative but can be qualitative as well in part i here we mainly study two kinds of steady state solutions which determine the dynamics of the model one consists of finite functions while the other consists of generalized functions which satisfy u v 0 on the part of the domain that b x vanishes but are positive and finite on the rest of the domain and are determined by certain boundary blow up systems the research is continued in part ii where these two kinds of steady state solutions will be used to determine the dynamics of the model

existence stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations abstract in this paper we study the existence stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise we first prove the existence and uniqueness of tempered random attractors for the stochastic equations and characterize the structures of the attractors by random complete solutions we then examine the existence and stability of random complete quasi solutions and establish the relations of these solutions and the structures of tempered attractors when the stochastic equations are incorporated with periodic forcing we obtain the existence and stability of random periodic solutions for the stochastic chafee infante equation we further establish the multiplicity and stochastic bifurcation of complete and periodic solutions

periodic solutions in an inhibitory two neuron network in this paper we consider a delayed network of two neurons with self feedback and interaction described by an all or none threshold function the discontinuity of signal function makes it difficult to apply directly dynamical system we show that the dynamics of the network can be understood in terms of the iterations of a one dimensional map and we obtain the existence and attractivity of periodic solutions moreover because the network is a limiting case of the corresponding smooth system as the parameter tends to infinity the above results can act as the guide to the rich dynamics of the smooth system therefore our results have important significance in both theory and applications

monotone dynamical systems with dense periodic points abstract in this paper we prove a recent conjecture by m hirsch which says that if f is a discrete time monotone dynamical system with f a homeomorphism on an open connected subset of a finite dimensional vector space and the periodic points of f are dense in then f is periodic

design of observers for linear systems with unknown inputs with a straightforward treatment a design of reduced order observers is presented for linear systems with unknown inputs the observers are derived with a physical meaning some explanations are given within the framework of descriptor system observer design principles the conditions for the existence of the observers are presented some illustrative examples are included

a novel approach to the design of unknown input observers a novel state estimator design scheme for linear dynamical systems driven by partially unknown inputs is presented it is assumed that there is no information available about the unknown inputs and thus no prior assumption is made about the nature of these inputs a simple approach for designing a reduced order unknown input observer uio with pole placement capability is proposed by carefully examining the dynamic system involved and simple algebraic manipulations it is possible to rewrite equations eliminating the unknown inputs from part of the system and to put them into a form where it could be partitioned into two interconnected subsystems one of which is directly driven by known inputs only this makes it possible to use a conventional luenberger observer with a slight modification for the purpose of estimating the state of the system as a result it is also possible to state similar necessary and sufficient conditions to those of a conventional observer for the existence of a stable estimator and also arbitrary placement of the eigenvalues of the observer the design and computational complexities involved in designing uios are greatly reduced in the proposed approach

attractors in coherent systems of differential equations abstract attractors of cooperative dynamical systems are particularly simple for example a nontrivial periodic orbit cannot be an attractor and orbits are nowhere dense this paper provides characterizations of attractors for the wider class of coherent systems defined by the property that all directed feedback loops are positive several new results for cooperative systems are obtained in the process connections with biological models are discussed

critical points for finite fibonacci chains of point delta interactions and orthogonal polynomials for a one dimensional schrodinger operator with a finite number n of point delta interactions with a common intensity the parameters are the intensity the n 1 intercenter distances and the mass critical points are points in the parameters space of the hamiltonian where one bound state appears or disappears the study of critical points for hamiltonians with point delta interactions arranged along a fibonacci chain is shown to be closely related to the study of the so called fibonacci operator a discrete one dimensional schrodinger type operator which occurs in the context of tight binding hamiltonians these critical points are the zeros of orthogonal polynomials previously studied in the context of special diatomic linear chains with elastic nearest neighbor interaction properties of the zeros location asymptotic behavior gaps are investigated the perturbation series from the solvable periodic case is determined the measure which yields orthogonality is investigated numerically from the zeros it is shown that the transmission coefficient at zero energy can be expressed in terms of the orthogonal polynomials and their associated polynomials in particular it is shown that when the number of point delta interactions is equal to a fibonacci number minus 1 i e when the intervals between point delta interactions form a palindrome all the fibonacci chains at critical points are completely transparent at zero energy

brief paper input to state stability of switched systems and switching adaptive control in this paper we prove that a switched nonlinear system has several useful input to state stable iss type properties under average dwell time switching signals if each constituent dynamical system is iss this extends available results for switched linear systems we apply our result to stabilization of uncertain nonlinear systems via switching supervisory control and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide iss properties with respect to the estimation errors detailed illustrative examples are included

common quadratic lyapunov like functions with associated switching regions for two unstable second order lti systems in this paper we establish quadratic lyapunov like functions for qualitative analysis of switched systems specifically for a class of switched systems consisting of two unstable second order lti linear time invariant subsystems we explore in detail some necessary and sufficient conditions for the existence of common weakly quadratic lyapunov like functions with associated switching regions in r 2 plane the existence conditions and the construction of such quadratic lyapunov like functions are established by using the conic switching laws

a note on interval observer design for unknown input estimation this paper addresses the problem of interval observer design for unknown input estimation in linear time invariant systems although the problem of unknown input estimation has been widely studied in the literature the design of joint state and unknown input observers has not been considered within a set membership context while conventional interval observers could be used to propagate with some additional conservatism unknown inputs by considering them as disturbances the proposed approach allows their estimation under the assumption that the measurement noise and the disturbances are bounded lower and upper bounds for the unmeasured state and unknown inputs are computed numerical simulations are presented to show the efficiency of the proposed approach

bound states of n dimensional harmonic oscillator decorated with dirac delta functions bound state solutions of the schrodinger equation have been investigated for n dimensional n 2 harmonic oscillator potential decorated with any finite number p of dirac delta functions the potential is radially symmetric and given as where is are arbitrary real numbers r1 r2 rp and ri 0 we have demonstrated that addition of dirac delta functions lifts the accidental degeneracies of n dimensional harmonic oscillator energy levels and leaves only the degeneracy due to the radial symmetry explicit forms of bound state eigenfunctions and the eigenvalue equation are given for n l values where n is the space dimension and l is the degree of n dimensional spherical harmonics we have shown that for given n and l there are a countably infinite number of bound state energy levels which are continuous functions of is and at most p of them can be negative

connecting orbits from synchronous periodic solutions to phase locked periodic solutions in a delay differential system we consider a system of delay differential equations modelling the excitatory interaction of two identical neurons assuming the delay is sufficiently large we show that the closure of the forward extension w5 of a 5 dimensional leading unstable manifold of the trivial solution contains a phase locked periodic orbit and a synchronized periodic orbit and we classify the dynamics of the semiflow restricted to w5 we also obtain the precise information about the floquet multipliers of the synchronized periodic orbit which enables us to establish the existence of heteroclinic orbits from the synchronized periodic orbit to the phase locked orbit

carrying simplices in nonautonomous and random competitive kolmogorov systems abstract the purpose of this paper is to investigate the asymptotic behavior of positive solutions of nonautonomous and random competitive kolmogorov systems via the skew product flows approach it is shown that there exists an unordered carrying simplex which attracts all nontrivial positive orbits of the skew product flow associated with a nonautonomous random competitive kolmogorov system

on the symbiotic lotka volterra model with diffusion and transport effects abstract in this work we analyze the existence stability and multiplicity of coexistence states for a symbiotic lotka volterra model with general diffusivities and transport effects global bifurcation theory blowing up arguments for a priori bounds singular perturbation results singularity theory and fixed point index in cones are among the techniques used to get our results and to explain the drastic change of behavior exhibited by the dynamics of the model between the cases of weak and strong mutualism between the species our methodology works out to treat much more general classes of symbiotic models

interval observer design for continuous time switched systems under known switching and unknown inputs this paper deals with unknown input estimation for switched linear systems in an unknown but bounded error ubbe framework based on a known switching signal and under the fulfilment of the relati

differentially positive systems the paper introduces and studies differentially positive systems that is systems whose linearization along an arbitrary trajectory is positive a generalization of perron frobenius theory is developed in this differential framework to show that the property induces a conal order that strongly constrains the asymptotic behavior of solutions the results illustrate that behaviors constrained by local order properties extend beyond the well studied class of linear positive systems and monotone systems which both require a constant cone field and a linear state space

delay independent incremental stability in time varying monotone systems satisfying a generalized condition of two sided scalability monotone systems generated by delay differential equations with explicit time variation are of importance in the modeling of a number of significant practical problems including the analysis of communications systems population dynamics and consensus protocols in such problems it is often of importance to be able to guarantee delay independent incremental asymptotic stability whereby all solutions converge toward each other asymptotically thus allowing the asymptotic properties of all trajectories of the system to be determined by simply studying those of some particular convenient solution it is known that the classical notion of quasimonotonicity renders time delayed systems monotone however this is not sufficient alone to obtain such guarantees in this work we show that by combining quasimonotonicity with a condition of scalability motivated by wireless networks it is possible to guarantee incremental asymptotic stability for a general class of systems that includes a variety of interesting examples furthermore we obtain as a corollary a result of guaranteed convergence of all solutions to a quantifiable invariant set enabling time invariant asymptotic bounds to be obtained for the trajectories even if the precise values of time varying parameters are unknown

global analysis of a schistosomiasis infection model with biological control in this paper the global stability of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mammalian host and a competitor snail species is studied by constructing lyapunov functions and using properties of k monotone systems we derive the basic reproduction number r 0 for the deterministic model and establish that the global dynamics are completely determined by the values of r 0 we show that the disease can be eradicated when r 0 1 in the case where r 0 1 we prove the existence uniqueness and global asymptotic stability of an endemic steady state this mathematical analysis of the model gives insight about the epidemiological consequences of the introduction of a competitor resistant snail species

the levinson theorem the levinson theorem is a fundamental theorem in quantum scattering theory which shows the relation between the number of bound states and the phase shift at zero momentum for the schrodinger equation the levinson theorem was established and developed mainly with the jost function with the green function and with the sturm liouville theorem in this review we compare three methods of proof study the conditions of the potential for the levinson theorem and generalize it to the dirac equation the method with the sturm liouville theorem is explained in some detail references to development and application of the levinson theorem are introduced

symmetric functional differential equations and neural networks with memory we establish an analytic local hopf bifurcation theorem and a topological global hopf bifurcation theorem to detect the existence and to describe the spatial temporal pattern the asymptotic form and the global continuation of bifurcations of periodic wave solutions for functional differential equations in the presence of symmetry we apply these general results to obtain the coexistence of multiple large amplitude wave solutions for the delayed hopfield cohen grossberg model of neural networks with a symmetric circulant connection matrix

on the number of states bound by one dimensional finite periodic potentials bound states and zero energy resonances of one dimensional finite periodic potentials are investigated by means of levinson s theorem for finite range potentials supporting no bound states a lower bound for the reduced time delay at threshold is derived

phase translation group actions on strongly monotone skew product semiflows we establish a convergence property for pseudo bounded forward orbits of strongly monotone skew product semiflows with invariant phasetranslation group actions the results are then applied to obtain global convergence of certain chemical reaction networks whose associated systems in reaction coordinates are monotone as well as the dynamics of certain reactiondiffusion systems in time recurrent structure including periodicity almost periodicity and almost automorphy

systems of ordinary differential equations which generate an order preserving flow a survey of results this article consists of a survey of results concerning the qualitative behavior of solutions of systems of ordinary differential equations which generate an order preserving flow we restrict our consideration to partial orderings on r n induced by any one of its orthants a flow preserves ordering if any two solutions x t and y t are ordered x t leqq y t for all t 0 whenever x 0 leqq y 0 many of the important results for such systems have only recently been obtained principally by m w hirsch who pointed out the tendency of their solutions to converge to equilibrium less well known are some global geometric constraints on the stable manifold of an equilibrium and the existence of heteroclinic orbits connecting ordered equilibria a particularly striking result for this class of systems is the easily computable necessary and sufficient condition for stability of an equilibrium one of our main goals is to show that by allowing partial orderings on r n generated by orthants

finitely many sphere interactions in quantum mechanics nonseparated boundary conditions let h be the closure of the restriction of the three dimensional laplacian on the domain c 0 r3 where nj 1 k 0 rj and k 0 rj is a closed ball of radius rj centered at the origin in r3 it is well known that h is a closed symmetric operator with deficiency indices in this paper all self adjoint s a extensions of h are constructed these extensions contain as particular cases the quantum hamiltonian describing concentric and sphere interactions it is also shown that the s a extensions of h may be obtained as norm resolvent limits of momentum cutoff and scaled separable potentials

asymptotic behavior of strongly monotone time periodic dynamical processes with symmetry given a strongly monotone discrete time dynamical system tn x x n z in an open and order convex subset x of a separable strongly ordered banach space v and a compact connected metrizable group g whose action on x is monotone and commutes with t we prove under some reasonable additional hypotheses that the limit set x of every stable point x x consists of symmetric points only i e g w w for all w x and g g moreover the set of all unstable points is contained in a union of at most countably many lipschitz manifolds of codimension one in v where each manifold is invariant under t and the action of g this result is applied to the time periodic spatially independent irreducible cooperative system of n reaction diffusion equations u t d t u f t u for t x r1 rn with spatially periodic boundary conditions in rn and with an initial distribution u0 which is continuous and satisfies the boundary conditions if u0 is stable then u0 contains spatially constant functions only and the dynamics on u0 is given by the irreducible cooperative system of n odes dudt f t u for t r1 here t is the poincare map if n 1 then u0 is a single fixed point of t if n 2 then v0 is a single fixed point of t for each v0 u0

convergence to equilibrium on invariant d hypersurfaces for strongly increasing discrete time semigroups abstract convergence to equilibrium for every positive semi orbit of strongly increasing discrete time semigroups on strongly ordered spaces is proved the domain of the semigroup is assumed to be slightly more general than a closed order interval in a strongly ordered banach space which is continuously imbedded into a banach lattice the semigroup is assumed to be order compact and every positive semi orbit is assumed to be order bounded the crucial hypothesis is the ljapunov stability of all equilibria it is also proved that the set of equilibria is a simply ordered arc the key tools are invariant d hypersurfaces

instability of discontinuous traveling waves for hyperbolic balance laws abstract it is known that scalar hyperbolic conservation laws with source term and periodic initial value have a property of poincare bendixson type namely the solutions converge either to a constant state or to a periodic traveling wave which is necessarily discontinuous in this paper we show that generically with respect to the l 1 topology the solutions exhibit a behaviour of the former type we also show that while the rate of convergence to a constant state is exponential the convergence to a traveling wave can be arbitrarily slow

asymptotic behaviour of comparable skew product semiflows with applications the almost 1 cover lifting property of omega limit sets is established for nonmonotone skew product semiflows which are comparable to uniformly stable eventually strongly monotone skew product semiflows these results are then applied to study the asymptotic behavior of solutions to the nonmonotone comparable systems of odes reaction diffusion systems differential systems with time delays and semilinear parabolic equations

monotone semiflows in scalar non quasi monotone functional differential equations abstract by introducing a stronger than pointwise ordering conditions are found under which scalar functional differential equations generate monotone semiflows even if they are not quasi monotone typically the maximum delay must be the smaller the more quasi monotonicity is violated the theory of monotone semiflows is used to show that most solutions converge to equilibrium and that stability of equilibria is essentially the same as for ordinary differential equations

dynamics integrability and topology for some classes of kolmogorov hamiltonian systems in r 4 abstract in this paper we first give the sufficient and necessary conditions in order that two classes of polynomial kolmogorov systems in r 4 are hamiltonian systems then we study the integrability of these hamiltonian systems in the liouville sense finally we investigate the global dynamics of the completely integrable lotka volterra hamiltonian systems in r 4 as an application of the invariant subsets of these systems we obtain topological classifications of the 3 submanifolds in r 4 defined by the hypersurfaces a x y b z w c x 2 y d x y 2 e z 2 w f z w 2 h where a b c d e f w and h are real constants

error bounds in differentiation of noisy signals by high gain observers the error in estimating the derivative s of a noisy signal by using a high gain observer is studied and quantified the error is bounded in terms of the infinity norms of the noise and a derivative of the signal the error bound is independent of the frequency or derivatives of the noise guidelines are presented for the observer gain design when it is used for on line differentiation analytical and simulation results are presented

switched observers for switched linear systems with unknown inputs two state observers are designed for some classes of switched linear systems with unknown inputs the design of the proposed observers assumes that all switching subsystems fulfill a property of strong detectability that allows to implement suitable reduced order unknown input switched observers the synthesis of the observers is based on the feasibility of a certain system of lmis two main schemes are presented for the case when the set of possible unknown input distribution matrices are linearly dependent an observer is suggested that guarantees the asymptotic state reconstruction without imposing any slow switching dwell time constraint about the sequence of the switching times for the general case the existence of a minimal average dwell time for every switching sequence is assumed by appropriate lyapunov analysis the convergence of the state estimate is proven to be exponential in both cases simulation results confirm the predicted performance

scattering theory for finitely many sphere interactions supported by concentric spheres we study stationary scattering theory for finitely many sphere interactions formally given by the hamiltonian h j 1n j x rj and its generalizations to the case of interactions of the second type and interactions with nonseparated boundary conditions in a previous publication j math phys 29 660 664 1988 it was shown that the self adjoint hamiltonian h l r corresponding to h may be defined as a limit in norm resolvent convergence of a family he of local scaled short range hamiltonians in this paper we also study scattering theory corresponding to he and show that the scattering quantities associated with he converge to those of h l r as e 0

observers for linear systems with unknown inputs a direct design procedure of a full order observer for a linear system with unknown inputs is presented using straightforward matrix calculations some examples are given in these examples a reduced order observer is also derived it is shown that this may restrict the rate of convergence of some state estimates

properties of bound states of the schrodinger equation with attractive dirac delta potentials we have studied bound states of the schrodinger equation for an attractive potential with any finite number p of dirac delta functions in rn where n 1 2 3 the potential is radially symmetric for n 2 and is given as v r 2 2m pi 1 i r ri where i 0 r1 2l n 2 and none otherwise we have also proven that there are at most p positive roots for the equation x22 k 0 where x x11x21x12x22 mpmp 1 m1 and mi sl 2 r are the particular transfer matrices mentioned above

dynamics of smooth essentially strongly order preserving semiflows with application to delay differential equations abstract in this paper we introduce a class of smooth essentially strongly order preserving semiflows and improve the limit set dichotomy for essentially strongly order preserving semiflows generic convergence and stability properties of this class of smooth essentially strongly order preserving semiflows are then developed we also establish the generalized krein rutman theorem for a compact and eventually essentially strongly positive linear operator by applying the main results of this paper to essentially cooperative and irreducible systems of delay differential equations we obtain some results on generic convergence and stability the linearized stability of an equilibrium and the existence of the most unstable manifold in these systems the obtained results improve some corresponding ones already known

convergence and stability for essentially strongly order preserving semiflows abstract this paper is concerned with a class of essentially strongly order preserving semiflows which are defined on an ordered metric space and are generalizations of strongly order preserving semiflows for essentially strongly order preserving semiflows we prove several principles which are analogues of the nonordering principle for limit sets the limit set dichtomy and the sequential limit set trichotomy for strongly order preserving semiflows then under certain compactness hypotheses we obtain some results on convergence quasiconvergence and stability in essentially strongly order preserving semiflows finally some applications are made to quasimonotone systems of delay differential equations and reaction diffusion equations with delay and the main advantages of our results over the classical ones are that we do not require the delicate choice of state space and the technical ignition assumption

levinson s theorem for schrodinger operators with point interaction a topological approach in this note levinson theorems for schrodinger operators in r n with one point interaction at 0 are derived using the concept of winding numbers these results are based on new expressions for the associated wave operators

new generic quasi convergence principles with applications in this paper essentially strongly order preserving and conditionally set condensing semiflows are considered obtained is a new type of generic quasi convergence principles implying the existence of an open and dense set of stable quasi convergent points when the state space is order bounded the generic quasi convergence principles are then applied to essentially cooperative and irreducible systems in the forms of ordinary differential equations and delay differential equations giving some results of theoretical and practical significance

a system of coupled oscillators can have arbitrary prescribed attractors a system of coupled nonlinear oscillators is considered if the size n of this oscillator network is large enough then the model can have arbitrary prescribed attractors which can be defined by some finite dimensional flows one can effectively find a simple interaction between the oscillators which gives these prescribed attractors

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

multi valued characteristics and morse decompositions abstract a rapid growth of molecular and systems biology in recent years challenges mathematicians to develop robust modeling and analytical tools for this area we combine a theory of monotone input output systems with a classical theory of morse decompositions in the context of ordinary differential equations models of biochemical reactions we show that a multi valued input output characteristic can be used to define non trivial morse decompositions which provide information about a global structure of the attractor the previous work on input output characteristics is shown to apply locally to individual morse sets and is seamlessly incorporated into our global theory we apply our tools to a model of cell cycle maintenance we show that changing the strength of the negative feedback loop can lead to cessation of cell cycle in two different ways it can either lead to globally attracting equilibrium or to a pair of equilibria that attract almost all solutions

on the finite dimensional dynamical systems with limited competition the asymptotic behavior of dynamical systems with limited competition is investigated we study index theory for fixed points permanence global stability convergence everywhere and coexistence it is shown that the system has a globally asymptotically stable fixed point if every fixed point is hyperbolic and locally asymptotically stable relative to the face it belongs to a nice result is the necessary and sufficient conditions for the system to have a globally asymptotically stable positive fixed point it can be used to establish the sufficient conditions for the system to persist uniformly and the convergence result for all orbits applications are made to time periodic ordinary differential equations and reaction diffusion equations

complicated dynamics in scalar semilinear parabolic equations in higher space dimension abstract we study the dynamics of the boundary value problem ut lu g x u u x 1 u 0 2 where l is a second order uniformly elliptic operator and r n is diffeomorphic to the ball in r n n 2 the main result asserts that given any ck vector field v on r n 1 with v 0 0 one can adjust coefficients of l and the function g such that the corresponding problem 1 2 has an n 1 dimensional invariant manifold through the equilibrium u 0 and the taylor expansion at u 0 of the vector field representing the flow on this manifold coincides in appropriate coordinates with the taylor expansion of v up to k th order terms this result implies that a hyperbolic invariant n torus can be found in 1 2 if l and g are appropriately chosen this result also indicates that chaotic dynamics is likely to occur for some choices of l and g

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

attractors in strongly monotone flows where f is a c vector field in r and all the off diagonal terms of its jacobian matrix are nonnegative the well known kamke theorem implies that the flow 4 i ir0 generated by 1 has the property it preserves the partial ordering 0 another system which has this property is the semilinear parabolic equation on a compact n dimensional submanifold solutions of its dirichlet or neumann problem determine a monotone flow in appropriate function space see 11 or 51 in general a flow which preserves a partial ordering on the state space is called monotone m w hirsch has studied this flow in a series of papers 14 io he 2 31 has studied the limiting behavior and convergence of solutions of system 1 he 1 4 lo has investigated this flow in the considerably abstract state space in chapter iii of cl he has used two sections to discuss the properties of attractors for monotone flows and obtained some very important results he has shown that a monotone flow cannot have an attracting cycle see l corollary 2 41 and that every attractor must contain an equilibrium see cl theorem 3 11 in particular if the flow is strongly monotone he has shown that every attractor k contains an order stable equilibrium see 1 theorem 4 11 meanwhile if we suppose z is attracted to k but is not quasiconvergent then k contains two order stable equilibria p q such that p o z 4 q see cl theorem 4 31 the purpose of this paper is further to discuss the properties of attractors for strongly monotone flows we shall study when an o limit set can be an 210 0022 247x 91 3 00

a remarkable spectral feature of the schrodinger hamiltonian of the harmonic oscillator perturbed by an attractive δ interaction centred at the origin double degeneracy and level crossing we rigorously define the self adjoint hamiltonian of the harmonic oscillator perturbed by an attractive interaction of strength centred at 0 the bottom of the confining parabolic potential by explicitly providing its resolvent our approach is based on a coupling constant renormalization related to a technique originated in quantum field theory and implemented in the rigorous mathematical construction of the self adjoint operator representing the negative laplacian perturbed by the interaction in two and three dimensions the way the interaction enters in our hamiltonian corresponds to the one originally discussed for the free hamiltonian instead of the harmonic oscillator one by p s ba it should not be confused with the potential perturbation of the harmonic oscillator discussed e g in a recent paper by gadella glasser and nieto also introduced by p s ba as a perturbation of the one dimensional free laplacian and recently investigated in that context by golovaty hryniv and zolotaryuk we investigate in detail the spectrum of our perturbed harmonic oscillator the spectral structure differs from that of the one dimensional harmonic oscillator perturbed by an attractive interaction centred at the origin the even eigenvalues are not modified at all by the interaction moreover all the odd eigenvalues regarded as functions of exhibit the rather remarkable phenomenon called level crossing after first producing the double degeneracy of all the even eigenvalues for the value b being the beta function

interval observers for continuous time lpv systems with l 1 l 2 performance an approach to interval observer design for linear parameter varying lpv systems is proposed it is assumed that the vector of scheduling parameters in lpv models is not available for measurement two different interval observers are constructed for nonnegative systems and for a generic case stability conditions are expressed in terms of matrix inequalities which can be solved with respect to the observer gains using standard numerical solvers applying l 1 l 2 framework the robustness and estimation accuracy with respect to model uncertainty are analyzed the efficiency of interval estimation for lpv models is demonstrated through numerical experiments for a microfluidic system and an academic example

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

rapid fluctuations of chaotic maps on rn the iterates f n of a chaotic map f display heightened oscillations or fluctuations as n i ff is a chaotic interval map in one dimension then it is now known that the total variation of f n on that interval grows exponentially with respect to n g chen t huang y huang chaotic behavior of interval maps and total variations of iterates internat j bifur chaos 14 2004 2161 2186 however the characterization of chaotic behavior of maps in multi dimensional spaces is generally much more challenging here we generalize the definition of bounded variations for vector valued maps in terms of the hausdorff measure and then use it to study what we call rapid fluctuations on fractal sets in multi dimensional chaotic discrete dynamical systems the relations among rapid fluctuations strict turbulence and positive entropy are established for lipschitz continuous systems on general n dimensional euclidean spaces applications to planar monotone or competitive systems and triangular systems on the square are also given

asymptotic tracking for constrained monotone systems this note addresses tracking control of nonlinear discrete time monotone systems subject to input and state constraints forcing saturation on a previously designed controller may in general lead to destabilization or at least result in constraint violation and performance losses hereby it is shown that for a certain class of nonlinear monotone systems it is possible to design a static nonlinear output feedback which saturated among suitable state dependent bounds is able to guarantee constraint satisfaction and asymptotic tracking of piecewise constant references with a moderate online computational burden simulation experiments concerning the synthesis of a protein demonstrate the effectiveness of the proposed control strategy