persistence in nonautonomous predator prey systems with infinite delays this paper studies the general nonautonomous predator prey lotka volterra systems with infinite delays the sufficient and necessary conditions of integrable form on the permanence and persistence of species are established a very interesting and important property of two species predator prey systems is discovered that is the permanence of species and the existence of a persistent solution are each other equivalent particularly for the periodic system with delays applying these results the sufficient and necessary conditions on the permanence and the existence of positive periodic solutions are obtained some well known results on the nondelayed periodic predator prey lotka volterra systems are strongly improved and extended to the delayed case

periodicity in a delayed ratio dependent predator prey system abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio dependent predator prey system in a periodic environment

periodicity and attractivity of a ratio dependent leslie system with impulses a ratio dependent leslie system with impulses is studied by using a comparison theorem continuation theorem base on coincidence degree and constructing a suitable lyapunov function we establish sufficient and necessary conditions for the existence and global attractivity of periodic solution examples show that the obtained criteria are easily verifiable

concurrent forward bounding for distributed constraint optimization problems a distributed search algorithm for solving distributed constraints optimization problems dcops is presented the new algorithm scans the search space by using multiple search processes sps that run on all agents concurrently sps search in non intersecting parts of the global search space and perform branch bound search each search process sp uses the mechanism of forward bounding fb to prune efficiently its part of the global search space the concurrent forward bounding concfb algorithm enables all sps to share their upper bound across all parts of the global search space the number of concurrent sps is controlled dynamically by the concfb algorithm by performing dynamic splitting within each sp a dynamic variable ordering is employed in order to help control the balance of computational load among all agents and across different sps the concfb algorithm is evaluated experimentally and compared to all state of the art dcop algorithms the number of non concurrent logical operations non concurrent steps the total number of messages sent and cpu time are used as performance metrics the evaluation procedure considers different dcop problem types with a varying number of agents and different constraint graphs as problems become larger and denser concfb is shown to outperform all other evaluated algorithms by 2 3 orders of magnitude in all performance measures further evaluations comparing different variants of concfb provide important insights into the working of the algorithm and reveals the contribution of its different components

concurrent search for distributed csps a distributed concurrent search algorithm for distributed constraint satisfaction problems discsps is presented concurrent search algorithms are composed of multiple search processes sps that operate concurrently and scan non intersecting parts of the global search space each sp is represented by a unique data structure containing a current partial assignment cpa that is circulated among the different agents search processes are generated dynamically started by the initializing agent and by any number of agents during search in the proposed concdb algorithm all search processes perform dynamic backtracking as a consequence of backjumping a search space can be found unsolvable by a different search process this enhances the efficiency of the concdb algorithm concurrent dynamic backtracking is an asynchronous distributed algorithm and is shown to be faster than former algorithms for solving discsps experimental evaluation of concdb on randomly generated discsps demonstrates that the network load of concdb is similar to the network load of synchronous backtracking and is much lower than that of asynchronous backtracking the advantage of concurrent search is more pronounced in the presence of imperfect communication when messages are randomly delayed

a theoretical evaluation of selected backtracking algorithms abstract in recent years many new backtracking algorithms for solving constraint satisfaction problems have been proposed the algorithms are usually evaluated by empirical testing this method however has its limitations our paper adopts a different purely theoretical approach which is based on characterizations of the sets of search tree nodes visited by the backtracking algorithms a notion of inconsistency between instantiations and variables is introduced and is shown to be a useful tool for characterizing such well known concepts as backtrack backjump and domain annihilation the characterizations enable us to a prove the correctness of the algorithms and b partially order the algorithms according to two standard performance measures the number of nodes visited and the number of consistency checks performed among other results we prove the correctness of backjumping and conflict directed backjumping and show that forward checking never visits more nodes than backjumping our approach leads us also to propose a modification to two hybrid backtracking algorithms backmarking with backjumping bmj and backmarking with conflict directed backjumping bm cbj so that they always perform fewer consistency checks than the original algorithms

locating the phase transition in binary constraint satisfaction problems abstract the phase transition in binary constraint satisfaction problems i e the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solutions as the constraints become tighter is investigated by examining the behaviour of samples of randomly generated problems in contrast to theoretical work which is concerned with the asymptotic behaviour of problems as the number of variables becomes larger this paper is concerned with the location of the phase transition in finite problems the accuracy of a prediction based on the expected number of solutions is discussed it is shown that the variance of the number of solutions can be used to set bounds on the phase transition and to indicate the accuracy of the prediction a class of sparse problems for which the prediction is known to be inaccurate is considered in detail it is shown that for these problems the phase transition depends on the topology of the constraint graph as well as on the tightness of the constraints

global attractivity and oscillations in a periodic delay logistic equation abstract sufficient conditions are obtained for the global attractivity of a positive periodic solution of the delay logistic equation dx t dt r t x t 1 x t n k t where r and k are positive periodic functions of period and n is a positive integer sufficient conditions are also obtained for all solutions to be oscillatory about k

a generalization of lavoie s inequality concerning the sum of idempotent matrices abstract let a complex p x n matrix a be partitioned as a a 1 a 2 a k denote by a a and a respectively the rank of a the transpose of a and an inner inverse or a g inverse of a let a 14 be an inner inverse of a such that a 14 a is a hermitian matrix let b a 14 1 a 14 2 ak 14 and a i 1 k a i then the product of nonzero eigenvalues of ba or ab cannot exceed one and the product of nonzero eigenvalues of ba is equal to one if and only if either b a 14 or a i a j 0 for all i j i j 1 2 k the results of lavoie 1980 and styan 1981 are obtained as particular cases a result is obtained for k 2 when the condition a i 1 k a i is no longer true

forward bounding on pseudo trees for dcops and adcops abstract complete search algorithms for solving distributed constraint optimization problems dcops can be divided into two groups algorithms that use a pseudo tree and algorithms that do not use one the best performing algorithms that do not use a pseudo tree use some form of forward bounding in order to try and gain from both worlds a new algorithm which incorporates a hybrid approach of the two groups is presented the proposed algorithm pseudo tree forward bounding pt fb is shown to perform very well pt fb is next extended to be able to solve asymmetric dcops adcops here again its performance is better than its competitors an extensive experimental evaluation of the performance of each of the proposed algorithms is presented

covariance of moore penrose inverses with respect to an invertible matrix abstract given an invertible complex matrix t a description is given of those matrices a with moore penrose inverse a such that tat 1 ta t 1

global existence of periodic solutions in a class of delayed gause type predator prey systems where x t y t denote the population density of prey and predator at time t respectively g e p e and z s are assumed to satisfy appropriate conditions v a positive constant stands for the death rate of predator y in the absence of prey x we may think of this system as herbivores y grazing upon vegetation x which take time r to recover in view of the fact that many predator prey systems display sustained fluctuations for examples see freedman l it is thus desirable to construct predator prey models capable of producing nonconstant periodic solutions when r 0 1 1 reduces to the well known undelayed gause type or kolmogorov predator prey systems again see freedman l and the references cited theorein under some assumptions the resulting systems can have a unique limit cycle in the positive cone see kuang and freedman 2 and the references cited therein to the best of our knowledge about delayed population interaction models the existing literature establishes the existence of a periodic solution by hopf bifurcation argument or reduces the delayed systems to undelayed systems of higher dimensions therefore these existence results are generally local most of the existing results on the global existence of nonconstant periodic solutions in delayed equations deal with scalar equations with single discrete delay such as 13 101

an empirical study of phase transitions in binary constraint satisfaction problems abstract an empirical study of randomly generated binary constraint satisfaction problems reveals that for problems with a given number of variables domain size and connectivity there is a critical level of constraint tightness at which a phase transition occurs at the phase transition problems change from being soluble to insoluble and the difficulty of problems increases dramatically a theory developed by williams and hogg 44 and independently developed by smith 37 predicts where the hardest problems should occur it is shown that the theory is in close agreement with the empirical results except when constraint graphs are sparse

spatiotemporal dynamics in a delayed diffusive predator model in this paper we investigate the spatiotemporal dynamics of a delayed reaction diffusion leslie gower model based on the stability analysis we demonstrate that delayed feedback may generate hopf and turing instability under some conditions resulting in spatial patterns one of the most interesting findings is that the model exhibits complex pattern replication pure turing instability gives birth to spots spots stripes mixture stripes stripes holes mixture and holes patterns pure hopf instability to spiral wave pattern and hopf turing instability to chaotic wave pattern our results well extend the findings of spatiotemporal dynamics in the delayed reaction diffusion predator prey model and indicate that time delay play an important roles in pattern formation

periodicity in a generalized semi ratio dependent predator prey system with time delays and impulses abstract with the help of a continuation theorem based on coincidence degree theory we establish necessary and sufficient conditions for the existence of positive periodic solutions in a generalized semi ratio dependent predator prey system with time delays and impulses which covers many models appeared in the literature when the results reduce to the semi ratio dependent predator prey system without impulses they generalize and improve some known ones

environmental periodicity and time delays in a food limited population model abstract sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the food limited population system modelled by the equation n t r t k t n t m k t c t r t n t m where m is a nonnegative integer and k r c are continuous positive periodic functions of period

periodic solutions of delayed leslie gower predator prey models with the help of continuation theorem base on gaines and mawhin s coincidence degree sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for both the first and the second leslie gower predator prey models with distributed or state dependent delays

on lavoie s determinantal inequality abstract let the complex matrix a be partitioned into r blocks a a 1 a r and let b a 1 a r where the superscript plus denotes moore penrose inverse then det ab 1 with equality if and only if ab i the matrices a b ab and ba all have the same rank which is equal to the number of nonzero eigenvalues of ab these nonzero eigenvalues are all real and positive when rank a r1 rank ai then the product of the nonzero eigenvalues of ab cannot exceed 1 equality occurs if and only if b a

a note on idempotent matrices let h be an n n matrix and let the trace the rank the conjugate transpose the moore penrose inverse and a g inverse or an inner inverse of h be respectively denoted by trh h h h and h this note develops two results i the class of idempotent g inverse of an idempotent matrix and ii if h is an n n matrix and h trh then tr h2h h h and the equality holds iff h is idempotent this result is compared with the previous result of khatri 1983 and some consequences of i and ii are given

periodic solutions of periodic delay lotka volterra equations and systems abstract by using the continuation theorem of coincidence degree theory sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic lotka volterra equations and systems with distributed or state dependent delays our results substantially extend and improve existing results