stochastic stabilization and destabilization of nonlinear differential equations abstract this paper is concerned with the stochastic stabilization and destabilization of nonlinear differential equations which more precisely further develops the general theory of stochastic stabilization and destabilization that was studied by mao 1994 4 and appleby et al 2008 1 the proposed results are of substantial improvements and reveal the more fundamental principle for stochastic stabilization and destabilization of dynamical systems which is also verified with examples of application to mass action systems

dynamics of the deterministic and stochastic siqs epidemic model with non linear incidence the deterministic and stochastic siqs models with non linear incidence are introduced for deterministic model the basic reproductive rate r 0 is derived moreover if r 0 1 there exists a unique endemic equilibrium which is globally asymptotically stable for stochastic model sufficient condition for extinction of the disease that is regardless of the value of r 0 is presented in addition if the intensities of the white noises are sufficiently small and r 0 1 then there exists a unique stationary distribution to stochastic model numerical simulations are also carried out to confirm the analytical results

asynchronous distance between homologous dna sequences the distance between homologous dna sequences of two species is proposed to be 1 4 ln det p where p is the conditional probability matrix specifying the proportions of the various nucleotides in the second sequence corresponding to each of the four nucleotides in the first sequence a probability model is described which supports this choice of distance distance measures based on a constant evolutionary rate assumption are described and compared with the proposed measure sampling properties of both types of distance are examined and we conclude by applying the distance measures to mitochondrial dna sequences of the hominoids

permanence and extinction in nonlinear single and multiple species system with diffusion in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments average conditions are obtained for the permanence and extinction of the systems considered the results obtained in this paper generalize the main results of cui and chen the effect of diffusion on the time varying logistic population growth comput math appl 36 3 1998 1 9 permanence and extinction in logistic and lotka volterra systems with diffusion j math anal appl 258 2 2001 512 535

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

new criteria on persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching abstract this paper concerns persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching by using some novel stochastic analysis techniques sufficient criteria for the partial permanence and partial extinction are established some novel sufficient conditions on persistence in mean and extinction are also obtained nontrivial examples are provided to illustrate our results

on the periodic solutions of periodic multi species kolmogorov type competitive system with delays and feedback controls abstract in this paper we consider a periodic multi species kolmogorov type competitive system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive periodic solution of the system are obtained as application the existence of the positive periodic solution of a kind of nonlinear competitive model with delays and feedback controls is discussed

geometry of canonical correlation on the state space of a quantum system a riemannian metric is defined on the state space of a finite quantum system by the canonical correlation or kubo mori bogoliubov scalar product this metric is infinitesimally induced by the nonsymmetric relative entropy functional or the von neumann entropy of density matrices hence its geometry expresses maximal uncertainty it is proven that the metric is monotone under stochastic mappings however an example shows that it is not the only such riemannian metric this fact is remarkable because in the probabilistic case the markovian monotonicity property characterizes the fisher information metric the essential difference appears in the curvatures of a classical state space and a quantum one a conjecture is made that the scalar curvature is monotone with respect to the more mixed statistical partial order of density matrices furthermore an information inequality resembling the cramer rao inequality of classical statistics is established the inequality provides a lower bound for the c

a mean extinction time estimate for a stochastic lotka volterra predator prey model the investigation of interacting population models has long been and will continue to be one of the dominant subjects in mathematical ecology moreover the persistence and extinction of these models is one of the most interesting and important topics because it provides insight into their behavior the mean extinction time depends on the initial population size and satisfies the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients hence finding analytical solutions poses severe problems except in a few simple cases so we can only compute numerical approximations an idea already mentioned in sharp and allen 1998 1 in this paper we study a stochastic lotka volterra model allen 2007 2 p 149 we prove the nonnegative character of its solutions for the corresponding backward kolmogorov differential equation we propose a finite element method whose matlab code is offered in the appendix and finally we make a direct comparison between predictions and numerical simulations of stochastic differential equations sdes

extinction time for stochastic population models the analysis of interacting population models is the subject of much interest in mathematical ecology moreover the persistence and extinction of these models is one of the most interesting and important topics because it provides insight into their behavior the mean extinction time for stochastic population models considered in this paper depends on the initial population size and satisfies a stationary partial differential equation related to the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients in this communication we review several papers where we have proposed some numerical techniques in order to estimate the mean extinction time for stochastic population models besides we will compare the theoretical predictions and numerical simulations for stochastic differential equations sdes this work can be viewed as a unified review of the contributions de la hoz and vadillo 2012 de la hoz et al 2014 and doubova and vadillo 2014

asymptotic behaviour of the stochastic gilpin ayala competition models abstract in this paper we investigate a stochastic gilpin ayala competition system which is more general and more realistic than the classical lotka volterra competition system we discuss the asymptotic behaviour in detail of the stochastic gilpin ayala competition system and comparing the classical lotka volterra with gilpin ayala competition system we find that the latter has better properties

local equations for equivariant evolutionary models abstract phylogenetic varieties related to equivariant substitution models have been studied largely in the last years one of the main objectives has been finding a set of generators of the ideal of these varieties but this has not yet been achieved in some cases for example for the general markov model this involves the open salmon conjecture see 2 and it is not clear how to use all generators in practice motivated by applications in biology we tackle the problem from another point of view the elements of the ideal that could be useful for applications in phylogenetics only need to describe the variety around certain points of no evolution see 13 we produce a collection of explicit equations that describe the variety on a zariski open neighborhood of these points see theorem 5 4 namely for any tree t on any number of leaves and any degrees at the interior nodes and for any equivariant model on any set of states we compute the codimension of the corresponding phylogenetic variety we prove that this variety is smooth at general points of no evolution and if a mild technical condition is satisfied d claw tree hypothesis we provide an algorithm to produce a complete intersection that describes the variety around these points

dynamics of non autonomous stochastic gilpin ayala competition model with time varying delays in this paper the non autonomous stochastic gilpin ayala competition model with time dependent delay is considered we prove existence and uniqueness of the global positive solution and various properties of that solution such as boundedness moment and pathwise estimation extinction non persistence in time average and weak persistence in addition we give a special case of the considered system and impose its properties all studied features are natural requirements from the biological point of view furthermore examples with numerical simulations are given to illustrate our results

on competitive lotka volterra model in random environments focusing on competitive lotka volterra model in random environments this paper uses regime switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem subject to the random changes of the external environment it is demonstrated that the growth rates of the population sizes of the species are bounded above moreover certain long run average limits of the solution are examined from several angles a partial stochastic principle of competitive exclusion is also derived finally simple examples are used to demonstrate our findings

remarks on stochastic permanence of population models abstract this paper examines the asymptotic behavior of the stochastic lotka volterra model under markovian switching we show that the stochastic lotka volterra model is stochastically permanent moreover we give another type of stochastic permanence and consider the relationship of two types of stochastic permanence under white noise perturbation

stochastic kolmogorov type system with infinite delay abstract the paper considers a stochastic functional kolmogorov type population system with infinite delay under the general probability measures main aim is to show that the environment noise will not only suppress a potential population explosion but also make the solution be stochastically ultimately bounded and asymptotic stable moreover two stochastic functional lotka volterra equations as examples are provided to illustrate the main results

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

distances and riemannian metrics for multivariate spectral densities the paper is concerned with the practical problem of how to compare power spectral densities of multivariable time series for scalar time series several notions of distance divergences have been proposed and studied starting from the early 1970s while multivariable ones have only recently began to receive any attention in the paper two classes of divergence measures inspired by classical prediction theory are introduced these divergences naturally induce riemannian metrics on the cone of multivariable densities the metrics amount to the quadratic term in the divergence between infinitesimally close to each other power spectra for one of the two we provide explicit formulae for the corresponding geodesics and geodesic distance a close connection between the geometry of power spectra and the geometry of the fisher rao metric is noted

regularization and interpolation of positive matrices we construct certain matricial analogues of mass transport for positive definite matrices of equal trace the framework aims to devise ways of interpolating positive definite matrices that tradeoff between aligning up their eigenstructure and scaling the corresponding eigenvalues motivation for the work is provided by power spectral analysis of multivariate time series where linear interpolation between matrix valued power spectra generates push pop unrealistic and undesirable artifacts

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

stochastic mutualism model under regime switching with levy jumps abstract this paper is concerned with a stochastic mutualism model under regime switching with levy jumps to begin with the existence and uniqueness of the global positive solution is proved with any given positive initial value then the sufficient conditions for stochastic permanence are established the critical value between extinction and persistence in mean is also obtained in addition under some suitable conditions we proved that there is a unique stationary distribution for the system without levy jumps our method relies on the lyapunov function analysis and the fredholm alternative the results demonstrate that regime switching may contribute to the permanence but jump noise may suppress the permanence

dynamics in a periodic competitive model with stage structure in this paper we consider a time delayed periodic system which describes the competition among mature populations by appealing to theories of monotone dynamical systems periodic semiflows and uniform persistence we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion

persistence attractivity and delay in facultative mutualism abstract relations between persistence and ultimate boundedness of the solutions of the lotka volterra system dx t dt x t r 1 a 11 x t a 22 y t dy t dt y t r 2 a 21 x t a 22 y t modelling facultative mutualism with delayed responses are established and sufficient conditions are obtained for the global attractivity of the positive equilibrium of the delay system

convergence conditions for some classes of nonlinear systems abstract systems of differential equations with nonlinearities of a sector type and almost periodic perturbations are studied with the aid of the lyapunov direct method conditions are found under which the considered systems admit globally asymptotically stable almost periodic solutions moreover it is shown that the proposed approach permits us to derive new convergence conditions for some models of neural networks and generalized lotka volterra models of population dynamics an example is presented to demonstrate the effectiveness of the obtained results

matrix optimal mass transport a quantum mechanical approach in this paper we describe a possible generalization of the wasserstein 2 metric originally defined on the space of scalar probability densities to the space of hermitian matrices with trace one and to the space of matrix valued probability densities our approach follows a control theoretic optimization formulation of the wasserstein 2 metric having its roots in fluid dynamics and utilizes certain results from the quantum mechanics of open systems in particular the lindblad equation it allows determining the gradient flow for the quantum entropy relative to this matricial wasserstein metric

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

adaptive eigensubspace algorithms for direction or frequency estimation and tracking the authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator s practical implementations the general formulation of the proposed estimator results from an asymptotic argument which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure a highly parallel algorithm denoted the inflation method is introduced for the estimation of the noise subspace the simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than p a thompson s 1980 adaptive version of v f pisarenko s technique 1973 in estimating frequencies or directions of arrival doa of plane waves for tracking nonstationary parameters the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions

a representation theoretic approach to the calculation of evolutionary distance in bacteria in the context of bacteria and models of their evolution under genome rearrangement we explore a novel application of group representation theory to the inference of evolutionary history our contribution is to show in a very general maximum likelihood setting how to use elementary matrix algebra to sidestep intractable combinatorial computations and convert the problem into one of eigenvalue estimation amenable to standard numerical approximation techniques

permanence of a delayed non autonomous gilpin ayala competition model abstract in this paper we consider a delayed non autonomous n species gilpin ayala competitive system which is more general and more realistic then classical lotka volterra competition model by means of ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions for the permanence of the system it is shown that our result is the generalization of those of zhao et al j d zhao j f jiang a c lazer the permanence and global attractivity in a nonautonomous lotka volterra system nonlinear analysis real world applications 5 4 2004 265 276 our results also supplement the results of fan and wang m fan k wang global periodic solutions of a generalized n species gilpin ayala competition model computer and mathematics with applications 40 2000 1141 1151

global attractivity of an almost periodic n species nonlinear ecological competitive model abstract by using comparison theorem and constructing suitable lyapunov functional we study the following almost periodic nonlinear n species competitive lotka volterra model x i t x i t r i t j 1 n a i j t x j i j t j 1 n b i j t x j i j t i j t j 1 n c i j t x i i i t x j i j t a set of sufficient conditions is obtained for the existence and global attractivity of a unique positive almost periodic solution of the above model as applications some special competition models are studied again our new results improve and generalize former results examples and their simulations show the feasibility of our main results

permanence of a discrete nonlinear n species cooperation system with time delays and feedback controls a discrete nonlinear n species cooperation system with time delays and feedback controls is considered in this paper sufficient conditions which ensure the permanence of the system are obtained it is shown that these conditions are weaker than those of chen f d chen permanence of a discrete n species cooperation system with time delays and feedback controls appl math comput 186 2007 23 29 that is our investigation shows that the additional condition in chen s paper is not necessary

positive periodic solution of a kind of nonlinear food chain system a nonlinear periodic food chain predator prey model is proposed in this paper which can be seen as the modification of the traditional lotka volterra food chain system sufficient conditions which guarantee the existence of the positive periodic solution of the system are obtained

stochastic lotka volterra system with infinite delay this paper investigates a stochastic lotka volterra system with infinite delay whose initial data comes from an admissible banach space c r we show that under a simple hypothesis on the environmental noise the stochastic lotka volterra system with infinite delay has a unique global positive solution and this positive solution will be asymptotic bounded the asymptotic pathwise of the solution is also estimated by the exponential martingale inequality finally two examples with their numerical simulations are provided to illustrate our result

on a periodic multi species ecological model a periodic predator prey model with m predators and n preys is proposed in this paper which can be seen as the modification of the traditional lotka volterra model by using comparison theorem the ultimately bounded region of the system is obtained by using comparison theorem and brouwer fixed point theorem sufficient conditions with guarantee the existence of a positive periodic solution of the system is obtained finally by constructing a suitable lyapunov function some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of system the results obtained here generalized the main results of j d zhao w c chen global asymptotic stability of a periodic ecological model applied mathematics and computation 147 3 2004 881 892

asymptotic behavior of a stochastic non autonomous predator prey system with jumps in this paper a two species stochastic non autonomous food chain predator prey system with jumps is proposed and studied the asymptotic properties of the system are examined sufficient conditions for extinction non persistence in the mean weak persistence in the mean and weak persistence of the system are established results show that levy jumps are disadvantageous for the persistence of the populations furthermore we also show that the solution is stochastically ultimate bounded under certain conditions some examples together with numerical simulations are introduced to illustrate our main results

analysis of a stochastic autonomous mutualism model abstract an autonomous lotka volterra mutualism system with random perturbations is investigated under some simple conditions it is shown that there is a decreasing sequence k which has the property that if 1 1 then all the populations go to extinction i e lim t x i t 0 1 i n if k 1 k 1 then lim t x j t 0 j k 1 n whilst the remaining k populations are stable in the mean i e lim t t 1 0 t x i s d s a positive constant i 1 k if n 1 then all the species are stable in the mean sufficient conditions for stochastic permanence and global asymptotic stability are also established

dynamics of a stochastic lotka volterra model perturbed by white noise abstract this paper continues the study of mao et al investigating two aspects of the equation d x t diag x 1 t x n t b a x t d t x t d w t t 0 the first of these is to slightly improve results in x mao s sabais e renshaw asymptotic behavior of stochastic lotka volterra model j math anal 287 2003 141 156 concerning with the upper growth rate of the total quantity i 1 n x i t of species by weakening hypotheses posed on the coefficients of the equation the second aspect is to investigate the lower growth rate of the positive solutions by using lyapunov function technique and using a changing time method we prove that the total quantity i 1 n x i t always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower growth rate

stochastic lotka volterra models with multiple delays abstract this paper investigates the asymptotic behavior of the stochastic lotka volterra model with multiple delays by using certain matrix techniques some results on nonexplosion boundedness and pathwise estimation of the model are investigated

sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching in this paper we prove that a stochastic logistic population under regime switching controlled by a markov chain is either stochastically permanent or extinctive and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions in the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems of the population model finally we illustrate our conclusions through two examples

real time probabilistic covariance tracking with efficient model update the recently proposed covariance region descriptor has been proven robust and versatile for a modest computational cost the covariance matrix enables efficient fusion of different types of features where the spatial and statistical properties as well as their correlation are characterized the similarity between two covariance descriptors is measured on riemannian manifolds based on the same metric but with a probabilistic framework we propose a novel tracking approach on riemannian manifolds with a novel incremental covariance tensor learning ictl to address the appearance variations ictl incrementally learns a low dimensional covariance tensor representation and efficiently adapts online to appearance changes of the target with only computational complexity resulting in a real time performance the covariance based representation and the ictl are then combined with the particle filter framework to allow better handling of background clutter as well as the temporary occlusions we test the proposed probabilistic ictl tracker on numerous benchmark sequences involving different types of challenges including occlusions and variations in illumination scale and pose the proposed approach demonstrates excellent real time performance both qualitatively and quantitatively in comparison with several previously proposed trackers

stability in distribution of a stochastic predator prey system with s type distributed time delays abstract this paper concerns the dynamics of a stochastic predator prey lotka volterra system with s type distributed time delays sufficient conditions for the stability in distribution of the solutions sds to the system are obtained the results show that the dynamic scenarios of the sds are completely characterized by two parameters 1 2 among which 1 is just related to the environmental noise while 2 is closely related to both time delays and environmental noises if 2 0 then the distributions of prey predator converge weakly to a unique ergodic invariant distribution ueid if 1 0 2 then the predator goes to extinction while the distributions of prey converge weakly to a ueid if 0 1 then both the predator and prey go to extinction

positive periodic solutions of nonautonomous functional differential systems abstract considered is the periodic functional differential system with a parameter x t a t x t x t f t x t using the eigenvalue problems of completely continuous operators we establish some criteria on the existence of positive periodic solutions moreover we apply the results to a couple of population models and obtain sufficient conditions for the existence of positive periodic solutions which are compared with existing ones

permanence of a nonlinear prey competition model with delays abstract a nonlinear periodic predator prey model with m preys and n m predators and delays is studied which can be seen as the modification of the traditional lotka volterra prey competition model two sets of sufficient conditions which guarantee the permanence of the system are obtained one set is delay independent while the other set is delay dependent our results supplement those obtained by chen et al f d chen x d xie j l shi existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays journal of computational and applied mathematics 194 2 2006 368 387

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

the effects of time dependent delays on global stability of stochastic lotka volterra competitive model abstract in this paper a stochastic lotka volterra competitive model with time dependent delays is investigated sufficient conditions for global asymptotic stability of the positive equilibrium are established the obtained result demonstrates that time dependent delays have important impacts on the global asymptotic stability of the positive equilibrium of the considered system

the linear steklov method for sdes with non globally lipschitz coefficients we present an explicit numerical method for solving stochastic differential equations with non globally lipschitz coefficients a linear version of the steklov average under a split step formulation supports our new solver the linear steklov method converges strongly with a standard one half order also we present numerical evidence that the explicit linear steklov reproduces almost surely stability solutions with high accuracy for diverse application models even for stochastic differential systems with super linear diffusion coefficients

a different consideraton about the globally asymptotically stable solution of the periodic n competing species problem abstract we consider the volterra lotka equations for n competing species n 2 in which the right hand sides are periodic in time we show that conditions given by k gopalsamy j austral math soc ser b 27 1985 66 72 which imply the existence of a periodic solution with positive components also imply the uniqueness and asymptotic stability of the solution

stochastic gilpin ayala competition model with infinite delay abstract in this paper we study the stochastic gilpin ayala competition model with an infinite delay we verify that the environmental noise included in the model does not only provide a positive global solution there is no explosion in a finite time but this solution is also stochastically ultimately bounded we obtain certain asymptotic results regarding a large time behavior

global positive periodic solutions of periodic n species competition systems abstract in this paper an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized n species lotka volterra type and gilpin ayala type competition systems is obtained it improves a series of the well known sufficiency theorems in the literature about the problems mentioned above the method is based on a well known fixed point theorem in a cone of banach space this approach can be applied to more general competition systems

diagonal riccati stability and applications abstract we consider the question of diagonal riccati stability for a pair of real matrices a b a necessary and sufficient condition for diagonal riccati stability is derived and applications of this to two distinct cases are presented we also describe some motivations for this question arising in the theory of generalised lotka volterra systems

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

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

on hybrid competitive lotka volterra ecosystems abstract this paper is concerned with competitive lotka volterra model in random environments it uses regime switching diffusion to model the dynamic of population sizes of n different species in a ecosystem subject to the random changes of the external environment we show that the positive solution of the associated stochastic differential equation does not explode in finite time with probability 1 moreover we demonstrate that the solution is stochastically bounded continuous and has finite moments furthermore we obtain certain asymptotic results regarding large time behavior and present some numerical experimental results

asymptotic properties of stochastic hybrid gilpin ayala system with jumps this paper focuses on studying the dynamics of the stochastic gilpin ayala model under regime switching with jumps the aim is to analyze what happens under the perturbations of regime switching and jumps some asymptotic properties are investigated and sufficient conditions for stochastic permanence extinction non persistence in the mean and weak persistence are provided the critical value among the extinction non persistence in the mean and weak persistence is obtained our results demonstrate that the dynamics of the model have close relations with the jumps and the stationary distribution of the markov chain

stationary distribution and periodic solutions for stochastic holling leslie predator prey systems abstract the stochastic autonomous and periodic predator prey systems with holling and leslie type functional response are investigated for the autonomous system we prove that there exists a unique stationary distribution which is ergodic by constructing a suitable lyapunov function under relatively small white noise the result shows that stationary distribution doesn t rely on the existence and the stability of the positive equilibrium in the undisturbed system furthermore for the corresponding non autonomous system we show that there exists a positive periodic markov process under relatively weaker condition finally numerical simulations illustrate our theoretical results

on a nonlinear nonautonomous predator prey model with diffusion and distributed delay in this paper a nonlinear nonautonomous predator prey model with diffusion and continuous distributed delay is studied where all the parameters are time dependent the system which is composed of two patches has two species the prey can diffuse between two patches but the predator is confined to one patch we first discuss the uniform persistence and global asymptotic stability of the model after that by constructing a suitable lyapunov functional some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained an example shows the feasibility of our main results

on a delayed nonautonomous ratio dependent predator prey model with holling type functional response and diffusion abstract a two species periodic ratio dependent predator prey model with holling type functional response and diffusion is investigated three different sets of sufficient conditions one set is diffusive independent and the other two sets are diffusive dependent which ensure the permanence of the system and a set of sufficient condition which ensure the extinction of the predator species are obtained examples together with their numeric simulations show the feasibility of the main results

smooth interpolation of covariance matrices and brain network estimation part ii we propose an approach to use the state covariance of autonomous linear systems to track time varying covariance matrices of nonstationary time series following concepts from the riemannian geometry we investigate three types of covariance paths obtained by using different quadratic regularizations of system matrices the first quadratic form induces the geodesics based on the hellinger bures metric related to optimal mass transport omt theory and quantum mechanics the second type of quadratic form leads to the geodesics based on the fisher rao metric from information geometry in the process we introduce a weighted omt interpretation of the fisher rao metric for multivariate gaussian distributions a main contribution of this work is the introduction of the third type of covariance paths which are steered by system matrices with rotating eigenspaces the three types of covariance paths are compared using two examples with synthetic data and real data from resting state functional magnetic resonance imaging respectively

coexistence states for periodic competitive kolmogorov systems abstract we prove the existence of positive periodic solutions for a class of nonautonomous competitive periodic kolmogorov systems which generalize the may leonard model a necessary and sufficient condition is also obtained

global attractivity in an almost periodic multi species nonlinear ecological model abstract a nonlinear almost periodic predator prey model with n preys and m predators is studied in this paper which can be seen as the modification of the traditional multi species lotka volterra predator prey model for general nonautonomous case by using the differential inequality theory we obtain the sufficient conditions which guarantee the uniform persistence and nonpersistence of the system after that by constructing a suitable lyapunov function some sufficient conditions are obtained which ensure the global attractivity of the system for almost periodic case by constructing a suitable lyapunov function sufficient conditions which guarantee the existence of an unique globally attractive positive almost periodic solution of the system are obtained examples together with their numeric simulations show the feasibility of our main results

permanence and extinction for a nonlinear diffusive predator prey system abstract in this paper we consider a non autonomous predator prey system in a poor patchy environment under the assumption that the intrinsic growth rates of the species may be negative sufficient conditions are obtained for the permanence and extinction of the system considered

almost periodic dynamics of a delayed three level food chain model abstractthis paper is concerned with the dynamics of a three level food chain model with time delays by means of mawhin s continuation theorem of coincidence degree theory we investigate the existence of positive almost periodic solutions in a three level food chain model with time delays a set of sufficient conditions for the existence of at least one positive almost periodic solution of the model is obtained in addition the global asymptotical stability of the almost periodic solution of the above model is also studied finally two examples and simulations are also given to illustrate the main results in this paper

orbits in a stochastic goodwin lotka volterra model abstract this paper examines the cycling behavior of a deterministic and a stochastic version of the economic interpretation of the lotka volterra model the goodwin model we provide a characterization of orbits in the deterministic highly non linear model we then study a stochastic version with brownian noise introduced via a heterogeneous productivity factor existence conditions for a solution to the system are provided we prove that the system produces cycles around a unique equilibrium point in finite time for general volatility levels using stochastic lyapunov techniques for recurrent domains numerical insights are provided

coexistence and exclusion of stochastic competitive lotka volterra models abstract this work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive lotka volterra model the conditions obtained are close to necessary in addition convergence in distribution of positive solutions of the model is also established a number of numerical examples are given to illustrate our results

stochastic lotka volterra systems with levy noise abstract this paper is concerned with stochastic lotka volterra models perturbed by levy noise firstly stochastic logistic models with levy noise are investigated sufficient and necessary conditions for stochastic permanence and extinction are obtained then three stochastic lotka volterra models of two interacting species perturbed by levy noise i e predator prey system competition system and cooperation system are studied for each system sufficient and necessary conditions for persistence in the mean and extinction of each population are established the results reveal that firstly both persistence and extinction have close relationships with levy noise secondly the interaction rates play very important roles in determining the persistence and extinction of the species

new conditions on the existence and stability of periodic solution in lotka volterra s population system in this paper we revisit the famous periodic lotka volterra competitive system some new and interesting sufficient conditions are obtained to guarantee the existence and global asymptotic stability of the periodic solution in the lotka volterra competitive system our method is based on mawhin s coincidence degree matrix s spectral theory and some new estimation techniques for the priori bounds of unknown solutions to the equation lx lambda nx due to this new method our new results are much different from the known results in the previous literature finally some examples and their simulations show the feasibility of our results

dynamic behaviors of a delay differential equation model of plankton allelopathy in this paper we consider a modified delay differential equation model of the growth of n species of plankton having competitive and allelopathic effects on each other we first obtain the sufficient conditions which guarantee the permanence of the system as a corollary for periodic case we obtain a set of delay dependent condition which ensures the existence of at least one positive periodic solution of the system after that by means of a suitable lyapunov functional sufficient conditions are derived for the global attractivity of the system for the two dimensional case under some suitable assumptions we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation examples show the feasibility of the main results

permanence and global attractivity of the discrete gilpin ayala type population model in this paper we propose a discrete gilpin ayala competition model and a discrete gilpin ayala type multispecies competition predator model for general nonautonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of an unique globally stable positive periodic solution of the system are obtained an example together with its numeric simulations shows the feasibility of the main results

evolution of predator prey systems described by a lotka volterra equation under random environment abstract in this paper we consider the evolution of a system composed of two predator prey deterministic systems described by lotka volterra equations in random environment it is proved that under the influence of telegraph noise all positive trajectories of such a system always go out from any compact set of int r 2 with probability one if two rest points of the two systems do not coincide in case where they have the rest point in common the trajectory either leaves from any compact set of int r 2 or converges to the rest point the escape of the trajectories from any compact set means that the system is neither permanent nor dissipative

the euler maruyama approximation for the asset price in the mean reverting theta stochastic volatility model stochastic differential equations sdes have been used to model an asset price and its volatility in finance lewis 2000 10 developed the mean reverting theta processes which can not only model the volatility but also the asset price in this paper we will consider the following mean reverting theta stochastic volatility model dx t a 1 m 1 x t dt s 1v t x t qdw 1 t dv t a 2 m 2 v t dt s 2v t bdw 2 t we will first develop a technique to prove the non negativity of solutions to the model we will then show that the em numerical solutions will converge to the true solution in probability we will also show that the em solutions can be used to compute some financial quantities related to the sde model including the option value for example

dynamic of a non autonomous predator prey system with infinite delay and diffusion in the present paper a nonlinear non autonomous predator prey dispersion model with continuous delay is studied sufficient conditions which guarantee the existence of a periodic positive solution are obtained by using gaines and mawhin s continuation theorem of coincidence degree theory moreover globally asymptotically stability of the system is also obtained by means of a suitable lyapunov functional the applications show that these criteria are easily verified

a comparative study of deterministic and stochastic dynamics for a non autonomous allelopathic phytoplankton model abstract in this paper we investigate a non autonomous competitive phytoplankton model with periodic coefficients in deterministic and stochastic environment respectively we prove the existence of at least one positive periodic solution together with it s global asymptotic stability the existence of periodic solution has been obtained by using the continuation theorem of coincidence degree theory proposed by gaines and mawhin we formulate the corresponding stochastic model by perturbing the growth rate parameters by white noise terms we prove that all the higher order moments of the solution to the stochastic system is uniformly bounded which ensure that the solution of the stochastic system is stochastically bounded we provide easily verifiable sufficient conditions for non persistence in mean extinction and stochastic permanence of the stochastic system sufficient condition for permanence shows that if the noise intensity is very low then the solution of the stochastic system persists in the periodic coexistence domain of the deterministic system we perform exhaustive numerical simulations to validate our analytical findings

periodicity in a nonlinear predator prey system on time scales with state dependent delays 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 nonlinear state dependent delays predator prey system on time scales

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained

network tomography based on additive metrics network tomography studies the inference of network structure and dynamics based on indirect measurements when direct measurements are unavailable or difficult to collect in this paper we design and analyze routing tree topology and link performance inference algorithms for communication networks using tools from phylogenetic inference in evolutionary biology we develop polynomial time distance based inference algorithms and derive sufficient conditions for the correctness of the algorithms we show that the algorithms are consistent and robust in particular the algorithms achieve the optimal l radius 1 2 for binary trees and 1 4 for general trees when a threshold neighbor selection criterion is used