multiple bifurcations in a delayed predator prey system with nonmonotonic functional response abstract a delayed predator prey system with nonmonotonic functional response is studied by using the normal form theory of retarded functional differential equations developed by faria and magalhaes the bifurcation analysis of the model indicates that there is a bogdanov takens singularity for any time delay value a versal unfolding of the model at the bogdanov takens singularity is obtained on the other hand it is shown that small delay changes the stability of the equilibrium of the model for some parameters and the system can exhibit hopf bifurcation as the time delay passes through some critical values

multiparametric bifurcation analysis of a basic two stage population model in this paper we investigate long term dynamics of the most basic model for stage structured populations in which the per capita transition from the juvenile into the adult class is density dependent the model is represented by an autonomous system of two nonlinear differential equations with four parameters for a single population we find that the interaction of intra adult competition and intra juvenile competition gives rise to multiple attractors one of which can be oscillatory a detailed numerical study reveals a rich bifurcation structure for this two dimensional system originating from a degenerate bogdanov takens bt bifurcation point when one parameter is kept constant depending on the value of this fixed parameter the corresponding triple critical equilibrium has either an elliptic sector or it is a topological focus which is demonstrated by the numerical normal form analysis it is shown that the canonical unfolding of the codimension three bt point reveals the underlying dynamics of

the smallest eigenvalues of the 1 point fixing graph abstract let s n be the symmetric group on 1 n the k point fixing graph f n k is defined to be the graph with vertex set s n and two vertices g h of f n k are joined if and only if g h 1 fixes exactly k points in this paper we determine the smallest eigenvalue for f n 1

bifurcation analysis of a predator prey system involving group defence a class of odes of generalized gause type modeling predator prey interaction is considered the prey are assumed to exhibit a phenomenon called group defence that is predation is decreased or even eliminated due to the ability of the prey to defend or disguise themselves as their numbers increase using the carrying capacity of the environment as the bifurcation parameter it is shown that the model undergoes a sequence of bifurcations that includes a homoclinic bifurcation as well as a hopf bifurcation conditions that hold even in the case of no group defence that ensure a subcritical hopf bifurcation and also the spontaneous appearance of a semistable periodic orbit that splits into a pair one stable and one unstable of periodic orbits are given ecological ramifications are considered unlike the classical model sufficient enrichment of the environment combined with group defence leads to extinction of the predator deterministically for almost all initial conditions providing strong support fo

global qualitative analysis of a non smooth gause predator prey model with a refuge abstract the present paper aims to provide a detailed qualitative analysis of a non smooth gause predator prey model in this model the saturating functional response function with a discontinuity at a critical prey density was employed to show the effects of a prey refuge on the population dynamic behavior analysis of this model revealed rich dynamics including locally or globally stable canard cycles a locally globally stable pseudo equilibrium unbounded trajectories in which both populations go to infinity or the prey goes to infinity and the predator dies out eventually the main purpose of the present work is to carry out a completely qualitative analysis for this model in particular two sets of sufficient conditions drive both populations to approach infinity and the sufficient and necessary conditions for all of the other main results are presented

the spectra of arrangement graphs abstract arrangement graphs were introduced for their connection to computational networks and have since generated considerable interest in the literature in a pair of recent articles by chen ghorbani and wong the eigenvalues for the adjacency matrix of an n k arrangement graph are studied and shown to be integers in this manuscript we consider the adjacency matrix directly in terms of the representation theory for the symmetric group our point of view yields a simple proof for an explicit formula of the associated spectrum in terms of the characters of irreducible representations evaluated on a transposition as an application we prove a conjecture raised by chen ghorbani and wong

canonical structure of soliton equations ii the kaup newell system abstract the canonical structure of the kaup newell system i e the family of the derivative nonlinear schrodinger equation and its generalizations is discussed

spectrum of cayley graphs on the symmetric group generated by transpositions abstract for an integer n 2 let x n be the cayley graph on the symmetric group s n generated by the set of transpositions 12 13 1 n it is shown that the spectrum of x n contains all integers from n 1 to n 1 except 0 if n 2 or n 3

on the eigenvalues of certain cayley graphs and arrangement graphs abstract in this paper we show that the eigenvalues of certain classes of cayley graphs are integers the n k r arrangement graph a n k r is a graph with all the k permutations of an n element set as vertices where two k permutations are adjacent if they differ in exactly r positions we establish a relation between the eigenvalues of the arrangement graphs and the eigenvalues of certain cayley graphs as a result the conjecture on integrality of eigenvalues of a n k 1 follows

conditional matching preclusion for the arrangement graphs the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex recently the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex it is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings in this paper we find this number and classify all optimal sets for the arrangement graphs one of the most popular interconnection networks

dynamics of a piecewise non linear system subject to dual harmonic excitation using parametric continuation abstract the dynamic behavior of piecewise linear and or non linear vibratory systems subject to a single harmonic excitation has been recently analyzed by using a one or multi term harmonic balance or galerkin s method piecewise linear techniques analog simulation and direct numerical integration digital simulation instead this paper proposes to utilize the technique of parametriccontinuationto study the steady state response and global dynamics of a two degree of freedom piecewise non linear system with backlash or multi valued springs and impact damping the physical system is under the influence of a mean load and is subject to a dual harmonic external excitation where the second frequency is either twice or three times the fundamental excitation frequency the effects of various parameters such as impact damping mean and alternating loads the piecewise stiffness ratios and the relative phase between the excitation harmonics on the system response are thoroughly examined system or excitation parameter regimes that exhibit sub harmonic super harmonic quasi periodic and chaotic solutions are obtained efficiently and systematically by using the proposed scheme this investigation also clarifies the differences between viscous and non linear impact damping models which have been proposed earlier in the literature for studying clearance non linearities limited experimental data validate our modelling strategy finally selected predictions from this technique match very well with a multi term harmonic balance method and with direct numerical integration wherever applicable

canonical structure of soliton equations i abstract the canonical structure of the nonlinear evolution equations in 1 1 dimensions solvable in terms of an n n inverse scattering problem is discussed the simplest form of the scattering problems that is those containing the spectral parameter linearly is considered it applies to most of the known soliton equations like the korteweg de vries eq the sine gordon eq and the boussinesq eq discussion of various possible reductions of the number of dependent variables by imposing constraints consistent with the hamiltonian flows is given together with the canonical structure of the reduced systems a direct proof of the involutive character of the infinite number of conserved quantities is given for the general case as well as the reduced case the relation between the conserved quantities and symmetry transformations lie backlund transformations becomes very simple in this framework

on the algebraic combinatorics of injections and its applications to injection codes we consider the algebraic combinatorics of the set of injections from a k element set to an n element set in particular we give a new combinatorial formula for the spherical functions of the gelfand pair s k times s n diag s k times s n k we use this combinatorial formula to give new delsarte linear programming bounds on the size of codes over injections

the number of shortest paths in the arrangement graph a solution to the shortest path enumeration problem can find numerous applications in studying issues related to interconnection networks in this paper we enumerate the number of shortest paths between any two vertices in an arrangement graph by establishing a bijection between these shortest paths and a collection of ordered forests of certain bi colored trees via minimum factorizations of permutations corresponding to such vertices in terms of so called arrangement transpositions and then count the number of these forests with the help of an existing result on the enumeration of such bi colored trees our result generalizes previous ones and can be applied to solve the same problem for other related graphs such as the alternating group graph on the other hand the techniques applied to derive such an enumeration result further extend the ongoing work of counting the number of minimum factorizations of a permutation in terms of a certain type of transposition a rather interesting problem in the area of algebraic combinatorics

cayley graph on symmetric group generated by elements fixing k points abstract let s n be the symmetric group on n 1 n the k point fixing graph f n k is defined to be the graph with vertex set s n and two vertices g h of f n k are joined if and only if g h 1 fixes exactly k points in this paper we derive a recurrence formula for the eigenvalues of f n k then we apply our result to determine the sign of the eigenvalues of f n 1

the spectrum of eigenvalues for certain subgraphs of the k point fixing graph abstract let s n be the symmetric group on n points the k point fixing graph f n k is defined to be the graph with vertex set s n and two vertices g h of f n k are joined if and only if g h 1 fixes exactly k points in this paper we give a recurrence formula for the eigenvalues of a class of regular subgraphs of f n k by using this recurrence formula we will determine the smallest eigenvalues for this class of regular subgraphs of f n 1 for sufficiently large n

global solvability of the derivative nonlinear schrodinger equation the derivative nonlinear schrodinger equation dnls iqt qxx q q2 x i q x t i a77xr z jffjt was first derived by plasma physicists 9 10 this equation was used to in terpret the propagation of circular polarized nonlinear alfven waves in plasma kaup and newell obtained the soliton solutions of dnls in 1978 5 the au thor obtained the local solvability of dnls in his dissertation 6 in this paper we obtain global existence in time of schwartz class solutions of dnls if the z 2 norm of the generic initial data q x 0 is bounded

on the dissipative evolution equations associated with the zakharov shabat system with a quadratic spectral parameter in this paper we derive some results for the zakharov shabat system of the form dm dx z2 j m zq p m j is diagonal and skewhermitian 8 10 12 following the idea of r beals and r r coifman we estimate the wedge products of the columns of m by l2 norm of the potential q p 4 by this result we have the global existence of the dissipative evolution equations associated with this spectral problem if the generic initial data q x 0 p x 0 qo po is of schwartz class 1 direct and inverse scattering for the z s system with a quadratic parameter by a potential here we mean a pair of functions q p r m c set of n x n complex matrices q is off diagonal and the diagonal part of p equals the diagonal part of q adj f q and q qx p p e l we consider the following spectral problem given z 0 x z im z o find m z r 4m c with 1 1 am z z 0x z 2 j m x z zq p m x z where j diag id id2 idn d 0 q z im z 0 for a certain set of potentials called generic m has the following properties 8 10 1 3 for any z e x there is a unique matrix v z such that for all x m x z m x z exp xz2j v z exp xz2j where m x z limit of m on i from q received by the editors may 4 1988 1980 mathematics subject classification 1985 revision primary 35q20 35q15

on the semiclassical limit of the general modified nls equation we study the semiclassical limit of the so called general modified nonlinear schrodinger equation for initial data with sobolev regularity before shocks appear in the limit system the strict hyperbolicity and genuine nonlinearity are proved for the dispersion limit of the cubic nonlinear case the limiting transition from the mnls equation to the nls equation is also discussed

threshold control strategy for a non smooth filippov ecosystem with group defense abstract a non smooth filippov ecosystem with group defense is proposed to investigate the effects of threshold and intermittent control strategy for ipm the proposed model has been analyzed theoretically using the qualitative analysis techniques related to filippov non smooth systems in the first place in particular the existence and stability of equilibria are discussed for the sliding mode dynamics through which it can be shown that the real equilibrium and pseudo equilibrium can coexist after that some relevant topics such as sliding mode bifurcation boundary focus bifurcation grazing bifurcation crossing bifurcation and buckling bifurcation are investigated using numerical analysis these complex sliding bifurcations reveal that the proposed filippov system admits the coexistence of multi attractors including equilibrium and crossing cycles thus indicating that there exists a close relationship between the intermittent control strategy and the initial densities of both populations similarly the global stability properties of real equilibrium and pseudo equilibrium of subsystems show that the intermittent control strategy can effectively control the pests under the prescribed threshold which is the aim of the ipm strategy