a generalization of volterra models with continuous time delay in population dynamics boundedness and global asymptotic stability we introduce a generalization of volterra models with continuous time delay by adding a nonnegative linear vector function of the species sufficient conditions for boundedness of solutions and global asymptotic stability of an equilibrium are provided applications from population dynamics are presented one concerns a predator prey volterra model with prey refuges and continuous time delay and another deals with a volterra system with currents of immigration for some species furthermore for this kind of model by a suitable homotopy function we provide a sufficient condition for the existence of the globally asymptotically stable equilibrium finally an example of a simple model in which two predators are competing for one prey which can take shelter is presented

dynamical systems with effective like potentials on etudie l existence des solutions t periodiques pour des systemes hamiltoniens d ordre 2 de la forme x v x ou v r n 0 r est de classe c 2 et v x quand x 0

radially symmetric systems with a singularity and asymptotically linear growth abstract we prove the existence of infinitely many periodic solutions for radially symmetric systems with a singularity of repulsive type the nonlinearity is assumed to have a linear growth at infinity being controlled by two constants which have a precise interpretation in terms of the dancer fucik spectrum our result generalizes an existence theorem by del pino et al 1992 4 obtained in the case of a scalar second order differential equation

the gbq algorithm for constructing start systems of homotopies for polynomial systems homotopy methods have become a standard tool for the computation of all solutions of a polynomial system this paper concerns the solution of deficient polynomial systems which appear to be typical in many engineering applications the gbq algorithm presented consists of two parts the computation of a generalized bezout number gb and the construction of a multi homogeneous start system q the approach generalizes m homogenization into multihomogenization it can also be regarded as a generalization towards the random product homotopy however without making assumptions on the coefficients of the polynomials in the system as is illustrated in the examples symmetric polynomial systems also can be solved more efficiently

on the multiple nevanlinna pick matrix interpolation in the class cp and the caratheodory matrix coefficient problem abstract in the present paper an intrinsic one to one correspondence between the finite multiple nevanlinna pick matrix interpolation np problem in the caratheodory class and the caratheodory matrix coefficient cc problem or equivalently the truncated trigonometric matrix moment tm problem is established thanks to this correspondence the np problem is reduced to what amounts to solving the cc problem or the tm problem associated with the so called toeplitz block vector of the former in both the nondegenerate and degenerate cases simultaneously

lie symmetries and invariants of the lotka volterra system in this paper we use the lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3d lotka volterra system

minimum w entropy interpolants for matricial caratheodory functions and maximum determinant completions of associated block pick matrix abstract the so called modified block toeplitz vector approach is used to connect a class of particular solutions g w for w d of a nondegenerate interpolation problem of the nevanlinna pick type with a class of particular solutions f w of a certain matricial caratheodory coefficient problem in a transparent way this will suggest a simple approach to the minimum w entropy interpolants and the maximum determinant completions of the associated block pick matrix within the framework of that nevanlinna pick type interpolation problem by using the known assertions corresponding to f w it turns out that g w w d is exactly or provides us with the unique solution to these two extremal problems in a manner

a neural network modeled by an adaptive lotka volterra system in this paper the asymptotic behavior of an n dimensional lotka volterra system with nonconstant coefficients that models the dynamics of an adaptive cellular network is analyzed each cell in the network is assumed to be connected to other cells in such a way that its output level of activity eitherinhibits or excites the growth of activity in the other cells the weight of the connection between any two cells varies over time in proportion to the average level of interaction between the two cells over the recent past if all of the connections are inhibitory it is shown that the network tends to produce a spontaneous and interesting classification of its inputs

symmetric homotopy construction abstract homotopy continuation methods can be applied to compute all finite solutions to a given polynomial system computations will be performed more efficiently if the symmetric structure of the system can be exploited this paper presents the construction of a symmetric homotopy using this homotopy only the paths according to the generating solutions have to be traced during continuation

on rank invariance of generalized schwarz pick potapov block matrices of matrix valued caratheodory functions abstract in view of a multiple nevanlinna pick interpolation problem we study the rank of generalized schwarz pick potapov block matrices of matrix valued caratheodory functions those matrices are determined by the values of a caratheodory function and the values of its derivatives up to a certain order we derive statements on rank invariance of such generalized schwarz pick potapov block matrices these results are applied to describe the case of exactly one solution for the finite multiple nevanlinna pick interpolation problem and to discuss matrix valued caratheodory functions with the highest degree of degeneracy

nontrivial solutions of operator equations and morse indices of critical points of min max type on montre que si les hypotheses du theoreme de point selle sont satisfaites si dim y 2 et si f 1 c contient seulement des points critiques non degeneres alors f 1 c contient au moins un point critique u 0 tel que 2 indice de morse u 0 dim y

sweeping algebraic curves for singular solutions many problems give rise to polynomial systems these systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters using predictor corrector methods we track the solution paths a point along a solution path is critical when the jacobian matrix is rank deficient the simplest case of quadratic turning points is well understood but these methods no longer work for general types of singularities in order not to miss any singular solutions along a path we propose to monitor the determinant of the jacobian matrix we examine the operation range of deflation and relate the effectiveness of deflation to the winding number computational experiments on systems coming from different application fields are presented

families of invariants of the motion for the lotka volterra equations the linear polynomials family the modified carleman embedding method already introduced by the authors to find first integrals invariants of the motion of polynomial form to the lotka volterra system is described in detail and its efficiency to treat the n dimensional system proved using this method an extensive investigation is performed for polynomials of the first degree which allow a classification of the integrals in three families for some systems possessing one invariant it is possible to find a second invariant using rescaling methods they represent very restrictive solutions implying that there exists a great number of conditions among the equation s coefficients to satisfy a proof is given that the volterra invariants can be deduced as a limit finally the interesting properties of the solutions of these systems are studied in detail

positive solutions to a singular neumann problem abstract we show the existence of positive solution for the following class of singular neumann problem u a x u h x u p in b r with u 0 on b r where r 0 0 is a positive parameter 0 p 0 1 b r b r 0 r n a b r r and h b r r are radially symmetric nonnegative c 1 functions using variational methods and sub and supersolutions we obtain a solution for an approximated problem involving mixed boundary conditions the limit of the approximated solutions is a positive solution

a neumann problem with logarithmic nonlinearity in a ball abstract the nonlinear elliptic problem u log u h x u p in a ball b r r n with neumann boundary conditions u 0 on b r were studied by means of a double perturbation argument we obtain a positive radial solution u c 2 b r 0 c b r

phase portraits of cubic polynomial vector fields of lotka volterra type having a rational first integral of degree 2 we classify all the global phase portraits of the cubic polynomial vector fields of lotka volterra type having a rational first integral of degree 2 for such vector fields there are exactly 28 different global phase portraits in the poincare disc up to a reversal of sense of all orbits