a computational method for finding all the roots of a vector function based on dynamical systems theory a computational method is proposed to locate all the roots of a nonlinear vector function the computational approach utilizes the cell mapping method this method relies on discretization of the state space and is a convenient and powerful numerical tool for analyzing the global behavior of nonlinear systems our study shows that it is efficient and effective for determining roots because it minimizes and simplifies computations of system trajectories since the roots are asymptotically stable equilibrium points of the autonomous dynamical system it also provides the domains of attraction associated with each root other numerical techniques based on iterative and homotopic methods can make use of these domains to choose appropriate initial guesses singular manifolds play an important role in limiting the extent of these domains of attraction both a theoretical basis and a computational algorithm for locating the singular manifolds are also provided they make use of similar state space discretization frameworks examples are given to illustrate the computational approaches it is demonstrated that for one of the examples a mechanical system the method yields many more solutions than those previously reported

lieb thirring inequality with semiclassical constant and gradient error term abstract in 1975 lieb and thirring derived a semiclassical lower bound on the kinetic energy for fermions which agrees with the thomas fermi approximation up to a constant factor whenever the optimal constant in their bound coincides with the semiclassical one is a long standing open question we prove an improved bound with the semiclassical constant and a gradient error term which is of lower order

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

dirichlet problem for the diffusive nicholson s blowflies equation abstract the object of this paper is to consider the asymptotic behavior of solutions of the diffusive nicholson s blowflies equation under dirichlet boundary condition a new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay when monotone or quasi monotone conditions fail to apply this approach should be applicable to other dirichlet problems as well even though our analysis is tailored to the diffusive nicholson s blowflies equation

nonlinear optimization exclusion tests for finding all solutions of nonlinear equations abstract exclusion tests are a well known tool in the area of interval analysis for finding the zeros of a function over a compact domain recently k georg developed linear programming exclusion tests based on taylor expansions in this paper we modify his approach by choosing another objective function and using nonlinear constraints to make the new algorithm converges faster than the algorithm in k georg a new exclusion test j comput appl math 152 2003 147 160 in this way we reduce the number of subinterval in each level the computational complexity for the new tests are investigated also numerical results and comparisons will be presented

slowly oscillating wave solutions of a single species reaction diffusion equation with delay we study positive bounded wave solutions u t x x ct 0 of equation ut t x u t x u t x g u t h x x rm this equation is assumed to have two non negative equilibria u1 0 and u2 0 the birth function g c r r is unimodal and differentiable at 0 and some results also require the feedback condition g s s c our results are based on a detailed geometric description of the wave profile in particular the monotonicity of its leading edge is established we also discuss the uniqueness problem indicating a subclass g of asymmetric tent maps such that given g g there exists exactly one positive travelling front for each fixed admissible speed

on an application of dynamical systems theory to determine all the zeros of a vector function abstract a continuous time dynamical system is constructed and analyzed in this paper to help locate all the zeros of nonlinear vector functions lyapunov stability technique is used to show that the zeros of the vector function become asymptotically stable equilibria for this dynamical system a strict lyapunov function is constructed to indicate local stability and to estimate the domains of attraction of all equilibria manifolds on which the jacobian of the vector field is singular play a significant role in characterizing the global behavior of the system examples are provided to illustrate the extent of the theory new computational techniques to determine all the zeros of a vector function can be developed based on the dynamical aspects of the theory given in this paper

wavefronts and global stability in a time delayed population model with stage structure we formulate and study a one dimensional single species diffusive delay population model the time delay is the time taken from birth to maturity without diffusion the delay differential model extends the well known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes this delayed model is known to have simple global dynamics similar to that of the logistic equation through the use of a sub supersolution pair method we show that the diffusive delay model continues to generate simple global dynamics this has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics we also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population connecting the zero solution of that equation with the positive steady state our main finding here is that our fronts appear to be all monotone regardless of the size of the delay this is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

a new exclusion test exclusion tests are a well known tool for obtaining all solutions of a nonlinear system of equations see e g the work of krawczyk or moore recently yamamura and collaborators have developed linear programming exclusion tests that turned out to be highly successful for nonlinear problems in electrical networking the author has developed higher order exclusion tests based on taylor expansions in the present paper it is shown that the ideas behind both approaches can be combined we present a new class of higher order linear programming exclusion tests investigate their computational complexity and illustrate their performance on several examples

a reaction diffusion model for a single species with age structure i travelling wavefronts on unbounded domains in this paper we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment we show that if the mature deat

existence and uniqueness of traveling waves for non monotone integral equations with applications abstract a class of integral equations without monotonicity is investigated it is shown that there is a spreading speed c 0 for such an integral equation and that its limiting integral equation admits a unique traveling wave up to translation with speed c c and no traveling wave with c c these results are also applied to some nonlocal reaction diffusion population models

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

a general cdc formulation for specializing the cell exclusion algorithms of finding all zeros of vector functions let j be the family of analytic compositions of analytic mappings and their absolute values a novel inequality on the range of the mappings in j is proved which is then used to yield a universal cdc cell discarded condition formulation for the system of equations f x 0 with f in j with this cdc formulation the cell exclusion algorithm developed in 1 is generalized it is shown that the algorithm generalized can not only be applied assuredly to locate all the zeros of any functions f in j but it can do so much more efficiently and conveniently than the original algorithms as well

evolution strategies with exclusion based selection operators and a fourier series auxiliary function abstract to improve the efficiencies of evolutionary algorithms eas we have proposed a highly efficient speed up strategy in our previous research work the exclusion based selection operators these operators could efficiently prevent the individuals of eas from getting into the attractions of local optima through the search space shrinking method however when a global optimum of a minimization problem is located in a very narrow attraction the exclusion based selection operators may not be able to find this narrow attraction and delete this global optimum mistakenly making the algorithm unreliable in this paper we propose a new complementary efficient speed up strategy the fourier series auxiliary function this strategy could guide an algorithm to search for optima with narrow attractions efficiently and effectively and compensate the deficiency of the exclusion based selection operators on the algorithm s reliability we combine these two strategies together to search the global optima in parallel one for optima in normal attractions and the other for optima in very narrow attractions respectively incorporation of these two strategies with any known evolutionary algorithm leads to an accelerated version of the algorithm as a case study the new strategies have been incorporated into evolution strategies es yielding an accelerated exclusion and fourier series auxiliary function es the efes the efes is experimentally tested with a test suite containing 10 complex multimodal function optimization problems and compared against the standard es ses and the fast es fes the experiments all demonstrate that the efes consistently and significantly outperforms other two es in efficiency and solution quality

lp narrowing a new strategy for finding all solutions of nonlinear equations an efficient algorithm is proposed for finding all solutions of systems of n nonlinear equations this algorithm is based on interval analysis and a new strategy called lp narrowing in the lp narrowing strategy boxes n dimensional rectangles in the solution domain containing no solution are excluded and boxes containing solutions are narrowed so that no solution is lost by using linear programming techniques since the lp narrowing is very powerful all solutions can be found very efficiently by numerical examples it is shown that the proposed algorithm could find all solutions of systems of 5000 50 000 nonlinear equations in practical computation time

a cell exclusion algorithm for determining all the solutions of a nonlinear system of equations abstract a new group of methods named cell exclusion algorithms ceas is developed for finding all the solutions of a nonlinear system of equations these types of algorithms different in principle from those of homotopy interval and cell mapping dynamical analysis approaches are based on cellular discretization and the use of a certain simple necessity test of the solutions the main advantages of the algorithms are their simplicity reliability and general applicability having all features of interval techniques but without using interval arithmetic and with complexity o log 1 e the algorithms improve significantly on both the interval algorithms and the cell mapping techniques theoretical analysis and numerical simulations both demonstrate that ceas are very efficient

travelling waves for delayed reaction diffusion equations with global response we develop a new approach to obtain the existence of travelling wave solutions for reaction diffusion equations with delayed non local response the approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain banach space coupled with an index formula of the associated fredholm operator and some careful estimation of the nonlinear perturbation the general result relates the existence of travelling wave solutions to the existence of heteroclinic connecting orbits of a corresponding functional differential equation and this result is illustrated by an application to a model describing the population growth when the species has two age classes and the diffusion of the individual during the maturation process leads to an interesting non local and delayed response for the matured population

dynamics of the diffusive nicholson s blowflies equation with distributed delay in this paper we study the diffusive nicholson s blowflies equation generalizing previous works we model the generation delay by using an integral convolution over all past times and results are obtained for general delay kernels as far as possible the linearized stability of the non zero uniform steady state is studied in detail mainly by using the principle of the argument global stability both of this state and of the zero state are studied by using energy methods and by employing a comparison principle for delay equations finally we consider what bifurcations are possible from the non zero uniform state in the case when it is unstable

existence of fast positive wavefronts for a non local delayed reaction diffusion equation abstract we establish the existence of a continuous family of fast positive wavefronts u t x x c t 0 for the non local delayed reaction diffusion equation u t t x u x x t x u t x r k x w g u t h w d w here 0 and 0 are fixed points of g c 2 r r and the non negative k is such that r k w e w d w is finite for every real we also prove that the fast wavefronts are non monotone if g h e h 1 1

a new exclusion test for finding the global minimum exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain these algorithms are based on a minimization condition that can be applied to each cell in the domain in this paper we consider lipschitz functions of order a and give a new minimization condition for the exclusion algorithm furthermore convergence and complexity results are presented for such algorithm

efficiency speed up strategies for evolutionary computation fundamentals and fast gas through identifying the main causes of low efficiency of the currently known evolutionary algorithms a set of six efficiency speed up strategies are suggested analyzed and partially explored including those of the splicing decomposable representation scheme the exclusion based selection operators the few generation ended ec search the low resolution computation with reinitialization and the coevolution like decomposition incorporation of the strategies with any known evolutionary algorithm leads to an accelerated version of the algorithm on the basis of problem space discretization the proposed strategies accelerate evolutionary computation via a best so far solution guided exclusion based space shrinking scheme with this scheme an arbitrarily high precision resolution solution of a high dimensional problem can be obtained by means of a successive low resolution search in low dimensional search spaces as a case study the developed strategies have been endowed with genetic algorithms gas yielding an accelerated genetic evolutionary algorithm the fast gas the fast gas are experimentally tested with a test suit containing 10 complex multimodal function optimization problems and a difficult real life problem the moment matching problem for inverse to the fractal encoding of the spleenwort fern the performance of the fast ga is compared against the standard ga sga and the forking ga fga that is one of the most recent and fairly established variants of gas the experiments all demonstrate that the fast gas consistently and significantly outperform the sga and fga in efficiency and solution quality in the test cases besides the speed up of efficiency other visible features of the fast gas include i no premature convergence occurs ii better convergence capability to global optimum and iii variable high precision solutions attainable all these support the validity and usefulness of the developed strategies

finding all solutions of separable systems of piecewise linear equations using integer programming abstract finding all solutions of nonlinear or piecewise linear equations is an important problem which is widely encountered in science and engineering various algorithms have been proposed for this problem however the implementation of these algorithms are generally difficult for non experts or beginners in this paper an efficient method is proposed for finding all solutions of separable systems of piecewise linear equations using integer programming in this method we formulate the problem of finding all solutions by a mixed integer programming problem and solve it by a high performance integer programming software such as glpk scip or cplex it is shown that the proposed method can be easily implemented without making complicated programs it is also confirmed by numerical examples that the proposed method can find all solutions of medium scale systems of piecewise linear equations in practical computation time

nonmonotone travelling waves in a single species reaction diffusion equation with delay abstract we prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction diffusion equations u t t x u t x u t x g u t h x when g c 2 r r has exactly two fixed points x 1 0 and x 2 k 0 recently nonmonotonic waves were observed in numerical simulations by various authors here for a wide range of parameters we explain why such waves appear naturally as the delay h increases for the case of g with negative schwarzian our conditions are rather optimal we observe that the well known mackey glass type equations with diffusion fall within this subclass of as an example we consider the diffusive nicholson s blowflies equation

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

positive heteroclinics and traveling waves for scalar population models with a single delay the existence of positive heteroclinic solutions is proven for a class of scalar population models with one discrete delay traveling wave solutions for scalar delayed reaction diusion equations are also obtained as perturbations of heteroclinic solutions of the associated equation without diusion as an illustration the results are applied to the nicholson s blowflies equation with diusion n t t x d 2n x2 t x n t x pn t x e an t x in the case of p e for which the nonlinearity is non monotone