bifurcation analysis of a generalized gause model with prey harvesting and a generalized holling response function of type iii abstract in this paper we study a generalized gause model with prey harvesting and a generalized holling response function of type iii p x m x 2 a x 2 b x 1 the goal of our study is to give the bifurcation diagram of the model for this we need to study saddle node bifurcations hopf bifurcation of codimension 1 and 2 heteroclinic bifurcation and nilpotent saddle bifurcation of codimension 2 and 3 the nilpotent saddle of codimension 3 is the organizing center for the bifurcation diagram the hopf bifurcation is studied by means of a generalized lienard system and for b 0 we discuss the potential integrability of the system the nilpotent point of multiplicity 3 occurs with an invariant line and can have a codimension up to 4 but because it occurs with an invariant line the effective highest codimension is 3 we develop normal forms in which the invariant line is preserved for studying of the nilpotent saddle bifurcation for b 0 the reversibility of the nilpotent saddle is discussed we study the type of the heteroclinic loop and its cyclicity the phase portraits of the bifurcations diagram partially conjectured via the results obtained allow us to give a biological interpretation of the behavior of the two species

identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

dynamical behavior of lotka volterra competition systems non autonomous bistable case and the effect of telegraph noise this article is concerned with the study of trajectory behavior of lotka volterra competition bistable systems and systems with telegraph noises we proved that for bistable systems there exists a unique solution bounded above and below by positive constants the oscillatory situation of systems with telegraph noises is pointed out

finite element approximation of a sixth order nonlinear degenerate parabolic equation we consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation equation here where generically equation here for any given equation here in addition to showing well posedness of our approximation we prove convergence in space dimensions d leq 3 furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed finally some numerical experiments in one and two space dimensions are presented

profile of the unique limit cycle in a class of general predator prey systems many predator prey systems with oscillatory behavior possess a unique limit cycle which is globally asymptotically stable for a class of general predator prey system we show that the solution orbit of the limit cycle exhibits the temporal pattern of a relaxation oscillator when a certain parameter is small

on global identifiability for arbitrary model parametrizations it is a fundamental problem of identification to be able even before the data have been analyzed to decide if all the free parameters of a model structure can be uniquely recovered from data this is the issue of global identifiability in this contribution we show how global identifiability for an arbitrary model structure basically with analytic non linearities can be analyzed using concepts and algorithms from differential algebra it is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression an explicit algorithm to test this is also given furthermore the question of persistent excitation for the input can also be tested explicitly is a similar fashion the algorithms involved are very well suited for implementation in computer algebra one such implementation is also described

hopf bifurcation of a predator prey system with stage structure and harvesting abstract in this paper a two species predator prey system with stage structure and harvesting is investigated the existence of hopf bifurcations of the system is given and the stability and directions of hopf bifurcations are determined by applying the normal form theory and the center manifold theorem

bifurcation analysis of modified leslie gower predator prey model with michaelis menten type prey harvesting abstract in the present paper we discuss bifurcation analysis of a modified leslie gower prey predator model in the presence of nonlinear harvesting in prey we give a detailed mathematical analysis of the model to describe some significant results that may arise from the interaction of biological resources the model displays a complex dynamics in the prey predator plane the permanence stability and bifurcation saddle node bifurcation transcritical hopf andronov and bogdanov takens of this model are discussed we have analyzed the effect of prey harvesting and growth rate of predator on the proposed model by considering them as bifurcation parameters as they are important from the ecological point of view the local existence and stability of the limit cycle emerging through hopf bifurcation is given the emergence of homoclinic loops has been shown through simulation when the limit cycle arising though hopf bifurcation collides with a saddle point this work reflects that the feasible upper bound of the rate of harvesting for the coexistence of the species can be guaranteed numerical simulations using matlab are carried out to demonstrate the results obtained

stochastic persistence and stationary distribution in a holling tanner type prey predator model abstract in this paper we study a stochastic predator prey model with beddington deangelis type functional response and logistic growth for predators the deterministic model is already well studied and we recall some important results here we construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations for the stochastic model we show that the system admits unique positive global solution starting from the positive initial value then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes finally we show that the system has a stationary distribution under certain parametric restrictions numerical simulations are carried out to substantiate the analytical results

chaotic dynamics of a three species prey predator competition model with noise in ecology in this paper we investigate a three species ecosystem consisting of a prey a predator and a top predator the predator survives on the prey and the top predator survives on both the prey and the predator the mathematical model consists of non linear simultaneous differential equations all the eight equilibrium points of the model are identified and by using routh hurwitz criteria as well as lyapunov function we derive the criteria for local and global stabilities also the population intensities of fluctuations variances around the positive equilibrium due to noise are computed their stability is also analyzed with computer simulation using matlab some numerical simulations for justifying the theoretical analysis are also provided the main conclusions are supplied in conclusion

stationary strategies for recursive games we study two person zero sum recursive matrix games framing them in the more general context of nonleavable games our aim is to extend a result of orkin orkin m 1972 recursive matrix games j appl probab 9 813 820 by proving that a uniformly e optimal stationary strategy is available to player i player ii in any recursive game such that the set where the value of the game is strictly greater less than its utility is finite the proof exploits some new connections between nonleavable and leavable games in particular we find sufficient conditions for the existence of e optimal stationary strategies for player i in a leavable game and we use these as a basis for constructing uniformly e optimal stationary strategies for the recursive games with which we are concerned

kalman filtering for a generalized class of nonlinear systems and a new gaussian quadrature technique the class of nonlinear systems treated in this technical note consists of the discrete time nonlinear systems that are formed by the interconnection of linear systems through static nonlinearities with few inputs this special structure is exploited to reduce the dimension of the integrals involved in the propagation of mean values and covariances thus permitting accurate calculations furthermore a new quadrature scheme suitable for nonlinear kalman filtering is introduced the proposed techniques are applied to a seven dimensional numerical example the results show that they can increase the performance significantly

bounded solutions and wavefronts for discrete dynamics this paper deals with the second order nonlinear difference equation dd r k dd u k q kg u k 1 0 where r k and q k are positive real sequences defined on n cup 0 and the nonlinearity g r to r is nonnegative and nontrivial sufficient and necessary conditions are given for the existence of bounded solutions starting from a fixed initial condition u 0 the same dynamic with f instead of g such that uf u 0 for u not 0 was recently extensively investigated on the contrary our nonlinearity g is of a small appearance in the discrete case its introduction is motivated by the analysis of wavefront profiles in biological and chemical models the paper emphasizes the many different dynamical behaviors caused by such a g with respect to the equation involving function f some applications in the study of wavefronts complete this work

global analysis in a predator prey system with nonmonotonic functional response a predator prey system with nonmonotonic functional response is considered global qualitative and bifurcation analyses are combined to determine the global dynamics of the model the bifurcation a

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

on the stability of non autonomous perturbed lotka volterra models the paper is devoted to an extended lotka volterra system of differential equations of predator prey model the extension is proposed with perturbation terms which are null for the positive equilibrium state in the original lotka volterra system the equilibrium state is not asymptotically stable due to the fact that perturbations are periodic in time the aim of the paper is to characterize a form of perturbation terms guaranteeing the asymptotic stability or instability of equilibrium state the reason of the proposed model is that for large time scale the lotka volterra model is too simple to be realistic in the paper the non autonomous perturbations do not change the equilibrium state but introduce functions of time as well as for additional perturbed terms as for the main part of the equations modified from lotka volterra model theorems are proposed in a renormalized form of the differential equations for time and the two variables the key point of the paper comes from the use of a liapunov function introduced in section 2 which allows to obtain conditions for the asymptotic stability section 3 and instability section 4 by using a cetaiev instability theorem following conditions on the renormalized coefficients in time of system 6 an appendix recalls the main results of the liapunov direct method for non autonomous binary systems of ordinary differential equations

dynamics of multi species competition predator system with impulsive perturbations and holling type iii functional responses abstract we investigate the dynamics of a class of multi species predator prey interaction models with holling type iii functional responses based on systems of nonautonomous differential equations with impulsive perturbations sufficient conditions for existence of a positive periodic solution are investigated by using a continuation theorem in coincidence degree theory which have been extensively applied in studying existence problems in differential equations and difference equations in addition sufficient criteria are established for the global stability and the globally exponential stability of the system by using the comparison principle and the lyapunov method

parametric identification of structured nonlinear systems in this paper identification of structured nonlinear systems is considered using linear fractional transformations lft the a priori information regarding the structural interconnection is systematically exploited a parametric approach to the identification problem is investigated where it is assumed that the linear part of the interconnection is given and the input to the nonlinear part is measurable an algorithm for the identification of the nonlinear part is proposed the uniqueness properties of the estimate provided by the algorithm are examined it is shown that the estimate converges asymptotically to its true value under a certain persistence of excitation condition two simulated examples and a real data example are presented to show the effectiveness of the proposed algorithm

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

topological degree in the generalized gause prey predator model abstract we consider a generalized gause prey predator model with t periodic continuous coefficients in the case where the poincare map p over time t is well defined the result of the paper can be explained as follows we locate a subset u of r 2 such that the topological degree d i p u equals to 1 the novelty of the paper is that the later is done under only continuity and some monotonicity assumptions for the coefficients of the model a suitable integral operator is used in place of the poincare map to cope with possible nonuniqueness of solutions the paper therefore provides a new framework for studying the generalized gause model with functional differential perturbations and multi valued ingredients

competing subcommunities of mutualist and a generalized kamke theorem a model of a biological community of species is considered the community consists of two competing subcommunities each of which has the property that each pair of species of the subcommunity interact in a mutually beneficial or noninterfering manner sufficient conditions are given that the two subcommunities can coexist the coexistence state being a stable equilibrium the domains of attraction of stable equilibria are considered the sharpest results are for the special case of lotka volterra systems mathematically the fundamental tool is a generalized kamke theorem

dynamics of a class of nonautonomous semi ratio dependent predator prey systems with functional responses abstract in this paper we investigate the dynamics of a class of the so called semi ratio dependent predator prey interaction models with functional responses based on systems of nonautonomous differential equations with time dependent parameters the functional responses are classified into five types and typical examples of each type are provided then we establish sufficient criteria for the boundedness of solutions the permanence of system and the existence uniqueness and globally asymptotic stability of positive periodic solution and positive almost periodic solution some conclusive discussion is presented at the end of this paper

identification of space time distributed parameters in the gierer meinhardt reaction diffusion system we consider parameter identification for the classic gierer meinhardt reaction diffusion system the original gierer meinhardt model a gierer and h meinhardt kybernetik 12 1972 pp 30 39 was formulated with constant parameters and has been used as a prototype system for investigating pattern formation in developmental biology in our paper the parameters are extended in time and space and used as distributed control variables the methodology employs pde constrained optimization in the context of image driven spatiotemporal pattern formation we prove the existence of optimal solutions derive an optimality system and determine optimal solutions the results of numerical experiments in two dimensions are presented using the finite element method which illustrates the convergence of a variable step gradient algorithm for finding the optimal parameters of the system a practical target function is constructed for the optimal control algorithm corresponding to the actual image of a marine angel

stability analysis on a predator prey system with distributed delays abstract this paper concerns the local and global dynamical properties of the nonnegative and positive equilibria of a lotka volterra predator prey system with distributed delays it is shown that while the positive equilibrium does not exist the nonnegative equilibrium is globally asymptotically stable or globally attractive as long as the delays are small enough if the positive equilibrium exists it is shown that it is locally asymptotically stable when the delays are suitably small furthermore an explicit asymptotic stability region for the positive equilibrium is also obtained based on a liapunov functional

combined effect of explicit time stepping and quadrature for curvature driven flows the flow of a closed surface of codimension 1 in bbb r n driven by curvature is first approximated by a singularly perturbed parabolic double obstacle problem with small parameter varepsilon 0 conforming piecewise linear finite elements with mass lumping over a quasi uniform and weakly acute mesh of size h are further used for space discretization and combined with forward differences for time discretization with uniform time step tau the resulting explicit schemes are the basis for an efficient algorithm the so called dynamic mesh algorithm and exhibit finite speed of propagation and discrete ondegeneracy no iteration is required not even to handle the obstacle constraints the zero level set of the fully discrete solution is shown to converge past singularities to the true interface provided tau h 2 approx o varepsilon 4 and no fattening occurs if the more stringent relations tau h 2 approx o varepsilon 6 are enforced then an interface rate of convergence o varepsilon is derived in the vicinity of regular points along with a companion o varepsilon 1 2 for type i singularities for smooth flows an interface rate of convergence of o varepsilonq is proven provided tau h 2 approx o varepsilon 5 and exact integration is used for the potential term the analysis is based on constructing fully discrete barriers via an explicit parabolic projection with quadrature which bears some intrinsic interest lipschitz properties of viscosity solutions of the level set approach and discrete nondegeneracy these basic ingredients are also discussed

the concept of force in population dynamics abstract the area of population dynamics has a rich history of the development and analysis of models of biological and social phenomena using ordinary differential equations this paper describes a method for understanding the influence one variable exerts on another in such models as a force with the relative effects of these forces providing a narrative explanation of the curvature in variable behaviour using the stock flow form of a model a symbolic notation is developed that identifies the forces with the causal pathways of the model s feedback loops a force is measured by its impact defined as the ratio of acceleration to rate of change computed by differentiation along its associated pathway between variables different phases of force dominance are determined to enhance the standard stability analysis of the models providing an explanation of model behaviour in newtonian mechanical terms the concepts developed are applied to well known models from mathematical biology the spruce budworm model where force dominance identifies scenarios that give clarity to intervention points and the lotka volterra predator prey model where the analysis highlights the importance of dissipative forces in achieving stability conclusions are drawn on the explanatory power of this approach with suggestions made for future work

identification of non linear systems using empirical data and prior knowledge an optimization approach abstract the choice of a parametric model structure in empirical and semi empirical non linear modeling is usually viewed as an important and critical step however it is known that by augmenting the least squares identification criterion with a term that imposes a penalty on the non smoothness of the model an optimal non parametric model can be found explicitly the optimal non parametric model will depend on the particular form of the penalty which can be looked upon as a priori knowledge or the desired properties of the model in this paper these results are extended in several directions i we show how useful types of prior knowledge other than smoothness can be included as a term in the criterion or as a constraint and how this influences the optimal model ii dynamic models and a general prediction error penalty are considered iii we present a practical numerical procedure for the identification of a close to optimal semi parametric model the numerical approach is motivated by the difficulty of deriving the optimal non parametric model if there are complicated constraints or penalty terms in the criterion and finally iv we discuss determination of the appropriate model complexity through selecting weights on the different penalties on the basis of empirical data since the optimal non parametric model is identified using an augmented optimization criterion and all prior knowledge and desired model properties may be specified through the augmented optimization criterion it is the choice of this criterion that is critical in this approach this elevates the empirical and semi empirical modeling problems to a more transparent and engineering friendly level than is achieved by directly specifying a parametric model structure hence our results shed some more light on modern non linear empirical modeling approaches like radial basis functions splines and neural networks in addition to providing a fundamental insight into the role of different kinds of prior knowledge this high level formulation is also attractive from a practical point of view as it lies closer to engineering thinking and less guesswork is required the flexibility and power of this approach are illustrated with a semi realistic simulation example

finite element approximation of a spatially structured metapopulation pde model abstract we present a new fully spatially structured pde metapopulation model for predator prey dynamics in d 3 space dimensions a nonlinear reaction diffusion system of rosenzweig macarthur form models predator prey dynamics in two high quality patches embedded in a low quality subdomain where species can diffuse convect and die our model substantially generalizes and improves earlier fully structured metapopulation models after a nondimensionalization procedure in order to approximate the metapopulation model we present a fully discrete galerkin finite element method in two space dimensions which is a generalization of the finite element method analyzed in a previous single patch predator prey model the numerical solutions are illustrated for some test cases using matlab numerical experiments demonstrate that the initial local extinction of predators in one patch leads to waves of recolonization from another patch in an appendix we also give an outline for the proof of the well posedness of the model

periodic solutions for a delayed predator prey system with stage structured predator on time scales in this paper a modified delayed predator prey system with stage structure for predator is proposed and studied which generalizes and incorporates as special cases some known models with the help of continuation theorem based on the gaines and mawhin coincidence degree theory we investigate the existence of periodic solutions for the proposed delayed predator prey system with stage structured predator and two kinds of functional responses called holling iii functional response and beddington deangelis functional response on time scales in particular when the time scale is chosen as the set of the real numbers or the integers the existence of the periodic solutions of the corresponding continuous time and discrete time models follows

test for local structural identifiability of high order non linearly parametrized state space models in this paper the issue of local structural identifiability of high order state space models with non linear parametrizations is addressed two methods are presented that provide analytical expressions for information matrices of which the rank determines identifiability the first method requires solving a lyapunov equation of high dimension and is applicable only to stable models the second method applies also to unstable models and is based on a gradient computation algorithm by dynamic programming that normally is used in an identification framework

borel stochastic games with lim sup payoff we consider two person zero sum stochastic games with limit superior payoff function and borel measurable state and action spaces the games are shown to have a value and the value function is calculated by transfinite iteration of an operator and proved to be upper analytic the paper extends results of our earlier article 17 in which the same class of games was considered for countable state spaces and finite action sets

existence of value and randomized strategies in zero sum discrete time stochastic dynamic games two players with conflicting objectives are simultaneously controlling a discrete time stochastic system the goal of this paper is to analyze such zero sum discrete time stochastic systems when the two players are allowed to use randomized strategies previous results have been restricted to systems with finite or compact state spaces such restrictions are usually untenable from the point of view of applications since many applications frequently use either the integers or mathbb r n as a state space our results are proved for complete separable metric spaces which are very useful for applications all previously known results emerge as special cases of our results in addition a variety of conjectures and open problems are resolved regarding the existence of a value function its properties such as borel measurability or continuity and the existence for either or both players of optimal or varepsilon optimal stationary strategies

identification of structured nonlinear systems this paper is concerned with the identification of static nonlinear components in a complex interconnected system these nonlinear components are treated nonparametrically in the sense that no natural parameterization is assumed to be available

persistence of periodic patterns for perturbed biological oscillators abstract we apply the perturbation method and the implicit function theorem to study the persistence of periodic patterns for two perturbed general biological oscillators one weakly coupled ordinary differential equation and one reaction diffusion system the proof relies also on the formal adjoint equation theory and the lyapunov schmidt method for the perturbed reaction diffusion model spatial temporal patterns such as rotating waves are shown to exist numerical simulations are presented to illustrate our analytical results

global attractivity in a periodic chemostat with general uptake functions a system of ode s is considered as a model of two populations competing for a nutrient where nutrient inputs and chemostat washouts are periodic as well general nutrient uptake functions which may also be time dependent and periodic are considered criteria are derived for there to exist a globally attracting positive periodic solution and a theorem on global monotonicity of attracting solutions between different systems is proved

concurrent reachability games we consider concurrent two player games with reachability objectives in such games at each round player 1 and player 2 independently and simultaneously choose moves and the two choices determine the next state of the game the objective of player 1 is to reach a set of target states the objective of player 2 is to prevent this these are zero sum games and the reachability objective is one of the most basic objectives determining the set of states from which player 1 can win the game is a fundamental problem in control theory and system verification there are three types of winning states according to the degree of certainty with which player 1 can reach the target from type 1 states player 1 has a deterministic strategy to always reach the target from type 2 states player 1 has a randomized strategy to reach the target with probability 1 from type 3 states player 1 has for every real e 0 a randomized strategy to reach the target with probability greater than email protected we show that for finite state spaces all three sets of winning states can be computed in polynomial time type 1 states in linear time and type 2 and type 3 states in quadratic time the algorithms to compute the three sets of winning states also enable the construction of the winning and spoiling strategies

on a prey predator reaction diffusion system with holling type iii functional response in this paper we study a prey predator model defined by an initial boundary value problem whose dynamics is described by a holling type iii functional response we establish global existence and uniqueness of the strong solution we prove that if the initial data are positive and satisfy a certain regularity condition the solution of the problem is positive and bounded on the domain q 0 t x w and then we deduce the continuous dependence on the initial data a numerical approximation of the system is carried out with a spectral method coupled with the fourth order runge kutta time solver the biological relevance of the comparative numerical results is also presented

efficient numerical methods for spatially extended population and epidemic models with time delay abstract reaction diffusion models with time delay have been widely applied in population biology as well as epidemiology this type of models can possibly exhibit complex dynamical behaviors such as traveling wave self organized spatial pattern or chaos numerical methods play an essential role in the study of these dynamical behaviors this paper concerns the finite element approximation for reaction diffusion models with time delay two fully discrete schemes and corresponding a priori error estimates are derived generally the research on evolution of population and epidemic needs to survey long time dynamical behaviors of these models so that it is important to improve the speed of numerical simulation to this end interpolation technique is used in our schemes to avoid numerical integration of reaction term an outstanding advantage of using interpolation of reaction term is that it improves the operation speed greatly meanwhile does not reduce convergence order applications are given to some model problems arising from population biology and epidemiology from these simulations some interesting phenomena can be found and we try to explain them in biological significance

instrumental variable methods for identification of hammerstein systems abstract consistency conditions for instrumental variable methods applied to hammerstein models are derived and analysed it is necessary to have a model that is not over parametrized and an input that is strongly persistently exciting i e the inputs and their powers are jointly persistently exciting some specific choices of the instruments are proved to give consistency those instruments are formed as filtered inputs and powers of the input consistency can be guaranteed if either the input is white noise or if a certain transfer function is positive real the vector of instruments is in general of larger dimension than the parameter vector it is shown then that a non singular linear transformation of the instruments gives a new and still consistent estimate some simulations using the iv variants proposed in this paper are also included

dynamics of a general prey predator model with prey stage structure and diffusive effects in this paper we propose and study the dynamics of a diffusive prey predator model with general functional response and stage structure for the prey firstly we consider the asymptotical stability of equilibrium points and hopf bifurcation for the reduced ode system secondly the existence and uniform boundedness of global solutions and stability of equilibrium points for the corresponding reaction diffusion system are discussed finally we establish the existence and the nonexistence of nonconstant positive steady states of this reaction diffusion system which indicates the effect of large diffusivity our results shows the importance of the diffusion rate of the predator species i e d 3 the large diffusion rate of the predator alone will help the generation of patterns however a large diffusion rate of the immature prey species or a large diffusion rate of the mature prey species can lead to the nonexistence of spatial patterns

input design for structured nonlinear system identification this paper is concerned with the input design problem for a class of structured nonlinear models this class contains models described by an interconnection of known linear dynamic systems and unknown static nonlinearities many widely used model structures are included in this class the model class considered naturally accommodates a priori knowledge in terms of signal interconnections under certain structural conditions the identification problem for this model class reduces to standard least squares we treat the input design problem in this situation an expression for the expected estimate variance is derived a method for synthesizing an informative input sequence that minimizes an upper bound on this variance is developed this reduces to a convex optimization problem features of the solution include parameterization of the expected estimate variance by the input distribution and a graph based method for input generation

qualitative analysis of a stochastic ratio dependent predator prey system a stochastic ratio dependent predator prey model is investigated in this paper by the comparison theorem of stochastic equations and ito s formula we obtain the global existence of a positive unique solution of the ratio dependent model besides a condition for species to be extinct is given and a persistent condition is established we also conclude that both the prey population and the ratio dependent function are stable in time average in the end numerical simulations are carried out to confirm our findings

uniqueness of circuits and systems containing one nonlinearity we study systems containing one memoryless nonlinearity we show that two such systems have the same i o operator only when they are related by simple scaling delay and loop transformations the theory is applied to one port networks containing one nonlinear element

analysis of autonomous lotka volterra competition systems with random perturbation abstract this paper discusses a randomized n species lotka volterra competition system we show that this system is stable in time average under certain conditions furthermore there is a stationary distribution of this system if extra conditions are satisfied also we give the extinction condition of this system finally numerical simulations are carried out to support our results

on the convergence of an iterative algorithm used for hammerstein system identification an analytical counterexample to the general convergence of an interative algorithm used for identification of hammerstein systems is given numerical illustration is also included

dynamics of age structured predator prey population models a predator prey model is investigated in which the prey population is assumed to have age structure and is governed by the mckendrick von foerster partial differential equation and the predator population is described by the classical volterra lotka ordinary differential equation quite general hypotheses are assumed for the mortality function the fertility function and the functional responses of predation existence and stability of three biologically meaningful equilibria corresponding to extinction of both species persistence of one species prey and coexistence of two species are studied a particular example and some numerical results are given

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

neimark sacker bifurcations in a non standard numerical scheme for a class of positivity preserving odes we discuss the nature of neimark sacker bifurcations occurring in a non standard numerical scheme for a class of positivity preserving systems of ordinary differential equations odes which undergoes a corresponding hopf bifurcation extending previous work alexander moghadas 2005a electron j diff eqn conf 12 9 19 it is shown that the type of neimark sacker bifurcation supercritical or subcritical may be affected by the integration time step the general form of the scheme in the vicinity of a fixed point is given from which the expression for the first lyapunov coefficient for two dimensional systems valid for arbitrary time step is explicitly derived the analysis shows that this coefficient undergoes an o shift with respect to the corresponding coefficient of the original ode this could lead to a type of bifurcation which differs from the corresponding hopf bifurcation in the ode due to changes in the sign of the first lyapunov coefficient as varies this is especially problematic in the vicinity of certain types of degenerate hopf bifurcation at which this coefficient may vanish we also present a general method to eliminate the possible o shift in the bifurcation parameter of the scheme however the first lyapunov coefficient may still be subjected to an o shift leading to a possibly erroneous type of bifurcation examples are given to illustrate the theoretical results of the paper with applications to mathematical biology

dynamics of a stochastic holling tanner predator prey model abstract in the paper we study a stochastic holling tanner predator prey system first by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solutions to the system after that sufficient causes for extinction of the predator population is obtained meanwhile we also obtain the threshold between persistence and extinction of the predator population at last some examples and numerical simulations are provided to illustrate our theoretical results

limit cycles for two families of cubic systems abstract in this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena the first one is motivated by a model of star formation histories in giant spiral galaxies and the second one comes from a model of volterra type to prove our results we develop a new criterion on the non existence of periodic orbits and we extend a well known criterion on the uniqueness of limit cycles due to kuang and freedman both results allow to reduce the problem to the control of the sign of certain functions that are treated by algebraic tools moreover in both cases we prove that when the limit cycles exist they are non algebraic

a three level finite element approximation of a pattern formation model in developmental biology this paper concerns a second order three level piecewise linear finite element scheme 2 sbdf ruuth in j math biol 34 148 176 1995 for approximating the stationary turing patterns of a well known experimental substrate inhibition reaction diffusion thomas system thomas in analysis and control of immobilized enzyme systems pp 115 150 1975 a numerical analysis of the semi discrete in time approximations leads to semi discrete a priori bounds and an optimal error estimate the analysis highlights the technical challenges in undertaking the numerical analysis of multi level ge 3 3 schemes we illustrate the effectiveness of the numerical method by repeating an important classical experiment in mathematical biology namely to approximate the turing patterns of the thomas system over a schematic mammal skin domain with fixed geometry at various scales we also make some comments on the correct procedure for simulating turing patterns in general reaction diffusion systems

homoclinic bifurcation of prey predator model with impulsive state feedback control abstract in this paper homoclinic bifurcations of a prey predator system with state impulse are investigated firstly the existence of order 1 homoclinic cycle of system 1 2 with 0 is investigated secondly choosing q as a control parameter the sufficient conditions of existence and stability of order 1 periodic solution of system 1 2 with 0 are obtained by means of the geometry theory of semi continuous dynamic systems thirdly on the basis of the theory of rotated vector fields homoclinic bifurcation of system 1 2 about parameter are also studied finally some simulations are provided to prove the main results the methods used in this paper are intuitive to prove the existence of order 1 homoclinic cycle and homoclinic bifurcations

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

periodic solutions and permanence for a delayed nonautonomous ratio dependent predator prey model with holling type functional response by using the continuation theorem of coincidence degree theory the existence of positive periodic solutions for a delayed ratio dependent predator prey model with holling type iii functional response x t x t a t b t t k t s x s ds c t x2 t y t m2y2 t x2 t y t y t e t x2 t m2y2 t x2 t d t is established where a t b t c t e t and d t are all positive periodic continuous functions with period 0 m 0 and k s is a measurable function with period is a nonnegative constant the permanence of the system is also considered in particular if k s 0 s where 0 s is the dirac delta function at s 0 our results show that the permanence of the above system is equivalent to the existence of positive periodic solution

identification of block oriented nonlinear systems starting from linear approximations a survey abstract block oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use many different identification approaches were developed over the years to estimate the parameters of a wide range of block oriented nonlinear models one class of these approaches uses linear approximations to initialize the identification algorithm the best linear approximation framework and the approximation framework or equivalent frameworks allow the user to extract important information about the system guide the user in selecting good candidate model structures and orders and prove to be a good starting point for nonlinear system identification algorithms this paper gives an overview of the different block oriented nonlinear models that can be identified using linear approximations and of the identification algorithms that have been developed in the past a non exhaustive overview of the most important other block oriented nonlinear system identification approaches is also provided throughout this paper

a multigrid preconditioned numerical scheme for a reaction diffusion system reaction diffusion operators have been used to model many engineering and biological systems in this study we consider a reaction diffusion system modeling various engineering and life science problems there are many algorithms to approximate such mathematical models most of the algorithms are conditionally stable and convergent for a big time step size a krylov subspace type solver for such models converges slowly or oscillates because of the presence of the diffusion term here we study a multigrid preconditioned generalized minimal residual method gmres for such a model we start with a five point scheme for the spatial integration and a method of lines for the temporal integration of the system of pdes then we implement a multigrid iterative algorithm for the full discrete model and show some numerical results to demonstrate the dominance of the solver we analyze the convergence rate of such a multigrid iterative preconditioning algorithm reaction diffusion systems arise in many mathematical models and thus this study has many applicabilities

existence of a polycycle in non lipschitz gause type predator prey models abstract we study gause type predator prey models when the interaction between predator and prey is not locally lipschitz continuous in the absence of one of them we shall show that in this case there appears a polycycle which affects the existence of limit cycles for the system we apply the results to study the existence of limit cycles for a classical gause system

dynamical and numerical analyses of a generalized food chain model this paper focuses on the qualitative and quantitative analysis of a generalized three species food chain model the conditions for the existence and stability of the boundary and positive equilibria of the model are established by constructing an appropriate bifurcation function it is shown that the model undergoes a hopf bifurcation from the positive equilibrium for certain parameter values the root of this bifurcation function gives the bifurcation value a robust non standard numerical method is constructed and used to obtain the solution of the model numerical simulations using this method show that the hopf bifurcation is supercritical with a stable limit cycle in the positive octant

numerical analysis of a first order in time implicit symplectic scheme for predator prey systems abstract the numerical solution of reaction diffusion systems modelling predator prey dynamics using implicit symplectic imsp schemes is relatively new when applied to problems with chaotic dynamics they perform well both in terms of computational effort and accuracy however until the current paper a rigorous numerical analysis was lacking we analyse the semi discrete in time approximations of a first order imsp scheme applied to spatially extended predator prey systems we rigorously establish semi discrete a priori bounds that guarantee positive and stable solutions and prove an optimal a priori error estimate this analysis is an improvement on previous theoretical results using standard implicit explicit imex schemes the theoretical results are illustrated via numerical experiments in one and two space dimensions using fully discrete finite element approximations

iterative scheme for the observation of a competitive lotka volterra system abstract in this work in terms of the model parameters sufficient conditions are established to construct a sequence of approximate observers for a two species competitive lotka volterra system this iterative approach makes it possible to localize the solution of the system and reveal its long term behaviour the main results are also illustrated by numerical simulations

lumped finite elements for reaction cross diffusion systems on stationary surfaces all the authors am is cv mf thank the isaac newton institute for mathematical sciences for its hospitality during the programme coupling geometric pdes with physics for cell morphology motility and pattern formation epsrc ep k032208 1 this work am has received funding from the european union s horizon 2020 research and innovation programme under the marie sklodowska curie grant agreement no 642866 am and cv acknowledge support from the engineering and physical sciences research council ep j016780 1 on modelling analysis and simulation of spatial patterning on evolving biological surfaces and the leverhulme trust research project grant rpg 2014 149 on unravelling new mathematics for 3d cell migration am was partially supported by a fellowship from the simons foundation am is a royal society wolfson research merit award holder generously funded by the wolfson foundation

singular perturbations of the holling i predator prey system with a focus abstract we study the occurrence of limit cyles in a model for two species predator prey interaction referred to as holling i this model is based on the phenomenological fitting of the so called functional response function to observed data in nature by a continuous piecewise differentiable function of the original models presented by holling it is the only model for which the possible asymptotic behaviour of the prey and predator densities has not been determined yet we extend the work of liu who showed that for certain values of parameters of the holling i system at least two nested limit cycles will occur surrounding a focus his case corresponds to a bifurcation problem where limit cycles are created from a system with a continuum of singularities i e a singular perturbation problem with slow fast solutions we prove that exactly two hyperbolic limit cycles occur after perturbation

optimal control of a nutrient phytoplankton zooplankton fish system we consider the mathematical formulation analysis and numerical solution of an optimal control problem for a nonlinear nutrient phytoplankton zooplankton fish reaction diffusion system we study the existence of optimal solutions derive an optimality system and determine optimal solutions in the original spatially homogeneous formulation m scheffer oikos 62 1991 pp 271 282 the dynamics of plankton were investigated as a function of parameters for nutrient levels and fish predation rate on zooplankton in our paper the model is spatially extended and the parameter for fish predation treated as a multiplicative control variable the model has implications for the biomanipulation of food webs in eutrophic lakes to help improve water quality in order to illustrate the control of irregular spatiotemporal dynamics of plankton in the model we implement a semi implicit in time finite element method with mass lumping and present the results of numerical experiments in two space dimensions

positive periodic solutions in a non selective harvesting predator prey model with multiple delays abstract this paper is concerned with a predator prey model with hassell varley type functional response non selective harvesting and multiple delays some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem in addition the results are delay dependent which is different from the previous work finally simulations illustrate the effectiveness of our results

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance

stability and bifurcation analysis on a ratio dependent predator prey model with time delay a ratio dependent predator prey model with time delay due to the gestation of the predator is investigated by analyzing the corresponding characteristic equations the local stability of a positive equilibrium and a semi trivial boundary equilibrium is discussed respectively further it is proved that the system undergoes a hopf bifurcation at the positive equilibrium using the normal form theory and the center manifold reduction explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions by means of an iteration technique sufficient conditions are obtained for the global attractiveness of the positive equilibrium by comparison arguments the global stability of the semi trivial equilibrium is also addressed numerical simulations are carried out to illustrate the main results

the basins of attraction in a modified may holling tanner predator prey model with allee affect abstract i analyse a modified may holling tanner predator prey model considering an allee effect in the prey and alternative food sources for predator additionally the predation functional response or predation consumption rate is linear the extended model exhibits rich dynamics and we prove the existence of separatrices in the phase plane separating basins of attraction related to oscillation co existence and extinction of the predator prey population we also show the existence of a homoclinic curve that degenerates to form a limit cycle and discuss numerous potential bifurcations such as saddle node hopf and bogdanov takens bifurcations we use simulations to illustrate the behaviour of the model

permanence and stability in non autonomous predator prey lotka volterra systems with feedback controls the main purpose of this article is considering whether or not the feedback controls have an influence on a non autonomous predator prey lotka volterra type system general criteria on permanence are established which is described by an integral form and independent of some feedback controls by constructing suitable lyapunov functionals a set of easily verifiable sufficient conditions are derived for the global stability of any positive solution to the model

dynamic analysis of fractional order singular holling type ii predator prey system abstract in this paper a fractional order singular fos predator prey model with holling type ii functional response has been introduced and the mathematical behavior of the model from the aspect of local stability is investigated through the fractional calculus and economic theory a new and more realistic predator prey model has been extended and the solvability condition is presented besides numerical simulations are considered to illustrate the effectiveness of the numerical method and confirm the theoretical results to explore the impacts of fractional order and economic interest on the presented system in biological context it is found that the presence of fractional order in the differential model can improve the stability of the solutions and enrich the dynamics of system in addition singular models exhibit more complicated dynamics rather than standard models especially the bifurcation phenomena which can reveal the instability mechanism of systems

finite element approximation of spatially extended predator prey interactions with the holling type ii functional response we study the numerical approximation of the solutions of a class of nonlinear reaction diffusion systems modelling predator prey interactions where the local growth of prey is logistic and the predator displays the holling type ii functional response the fully discrete scheme results from a finite element discretisation in space with lumped mass and a semi implicit discretisation in time we establish a priori estimates and error bounds for the semi discrete and fully discrete finite element approximations numerical results illustrating the theoretical results and spatiotemporal phenomena are presented in one and two space dimensions the class of problems studied in this paper are real experimental systems where the parameters are associated with real kinetics expressed in nondimensional form the theoretical techniques were adapted from a previous study of an idealised reaction diffusion system garvie and blowey in eur j appl math 16 5 621 646 2005

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection