induced i l fuzzy topological spaces abstract in this paper we introduce the notion of induced i l fuzzy topological spaces by using the i l valued lower semicontinuous mappings and investigate some of their basic properties in particular we give a necessary and sufficient condition for an i l fuzzy topological space to be induced and prove that this kind of induced space preserves the cartesian product and the n compactness as well

on the state minimization of fuzzy automata this paper investigates the minimization problem of fuzzy automata aiming to obtain a procedure for finding a minimal state fuzzy automaton equivalent to a given one the decision version of the minimization problem is as follows given a fuzzy automaton cal a and a natural number k i e a pair langle cal a k rangle is there a k state fuzzy automaton equivalent to cal a we prove that the above problem is decidable for fuzzy automata over totally ordered lattices and then obtain a procedure for minimizing a given fuzzy automaton to this end we introduce the concept of systems of fuzzy polynomial equations present a procedure for finding solutions of these systems and finally reduce the above decision problem to finding a solution of a system of fuzzy polynomial equations it is worth pointing out that although some algorithms in the literature were claimed to be minimization algorithms the term minimization there did not mean state minimization in our sense since these algorithms did not aim at a minimal fuzzy automaton but found reasonably small fuzzy automata

a categorical approach to minimal realization for a fuzzy language abstract in this study we provide a general theory of minimal realization for a given fuzzy language in a category theory setting we introduce categorical characterizations of a run map reachability map and observability map for a crisp deterministic fuzzy automaton finally we show that all minimal realizations for a given fuzzy language are isomorphic to the nerode realization for the same case

an insertion theorem for continuous valued functions and its consequences spaces in which open sets take values in the l interval i l are investigated we prove a theorem concerning the insertion of a continuous function with values in i l with l a complete lattice we establish certain factorizations of the functors i l and i l with l a hypercontinuous lattice the latter result and the insertion theorem provide a partial answer to a recent open question related to insertion of lattice valued functions as another application of the insertion theorem we establish a relation between complete regularity in the categories of l topological and i l topological spaces with l a frame

connectedness and local connectedness in lowen spaces a fuzzy connectedness axiom and a matching fuzzy local connectedness are defined in this paper for lowen spaces it is shown that such lowen spaces have properties corresponding to those of traditional connected and locally connected topological spaces it is also proved that an l topological space x d is fuzzy connected resp fuzzy locally connected in our sense if and only if its induced i l topological space x w d is too some related categorical results are also obtained and a fuzzy version of topological intersection theorems is given by using our notion of connectedness

permanence of dispersal population model with time delays permanence of a dispersal single species population model is considered where environment is partitioned into several patches and the species requires some time to disperse between the patches the model is described by delay differential equations the existence of food rich patches and small dispersions among the patches are proved to be sufficient to ensure partial permanence of the model it is also shown that partial permanence ensures permanence if each food poor patch is connected to at least one food rich patch and if each pair in food rich patches is connected furthermore it is proved that partial persistence is ensured even under large dispersion among food rich patches if the dispersion time is relatively small

determinization of fuzzy automata via factorization of fuzzy states fuzzy finite state automata over the algebra 0 1 max 0 1 in which the monoid 0 1 1 denotes a continuous triangular norm is not locally finite can accept fuzzy languages of infinite range for a given fuzzy finite state automaton which accepts a fuzzy language of infinite range we define the determinization of the fuzzy automaton via factorization of fuzzy states i e the computation of an equivalent deterministic fuzzy automaton whether it is finite this method of determinization is a generalization of the well known accessible subset construction our main contribution is to determine that the representable cycles property is the necessary and sufficient condition for determinization of a fuzzy finite state automaton via a maximal factorization of fuzzy states this property is more general than the twins property adapted for fuzzy automata which is the sufficient condition for weighted automata over the tropical semiring

grammar theory based on lattice ordered monoid motivated by li and pedrycz s work on fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids and inspired by the close relationship between the automata theory and the theory of formal grammars we have established a fundamental framework of l valued grammar it is shown that the set of l valued regular languages coincides with the set of l languages recognized by nondeterministic l fuzzy finite automata and every l language recognized by a deterministic l fuzzy finite automaton is an l valued regular language

induced i l fuzzy topological vector spaces abstract in this paper we introduce and study the induced i l fuzzy topological vector spaces the following main result is proved if l x is an l fuzzy topological vector space then i l x i l is an i l fuzzy topological vector space where i l is the fuzzy unit interval and i l is the induced i l fuzzy topology of the l fuzzy topology furthermore we also prove that the induced i l fuzzy topological vector spaces i l x i l preserve the product and quotient space as well

further improvements of determinization methods for fuzzy finite automata in this paper we provide further improvements of determinization methods for fuzzy finite automata these methods perform better than all previous determinization methods for fuzzy finite automata developed by b lohlavek 3 li and pedrycz 38 ignjatovic et al 25 and jancic et al 33 in the sense that they produce smaller automata while require the same computation time the only exception is the brzozowski type determinization algorithm developed recently by jancic and iric 34 which produces a minimal crisp deterministic fuzzy automaton but the algorithms created here can also be used within the brzozowski type algorithm and improve its performance

fuzzy languages with infinite range accepted by fuzzy automata pumping lemma and determinization procedure abstract the formulation of fuzzy automata allows us to select a great variety of triangular norms depending on the selected triangular norm a fuzzy automaton can accept a fuzzy language fa language with infinite range these fuzzy automata are not equivalent to the so called deterministic fuzzy automata deterministic automata with a fuzzy subset of final states which only accept fuzzy languages with finite range in this paper we study fa languages with infinite range and a determinization procedure in order to obtain an equivalent fuzzy deterministic automaton for a given fuzzy automaton a fuzzy deterministic automaton is a fuzzy automaton which satisfies the deterministic condition in its state transition function the main contributions of our paper are 1 a pumping lemma of fa languages with infinite range 2 the formulation of fuzzy deterministic automata and a pumping lemma of fda languages 3 the necessary conditions for the determinization of fuzzy automata under continuous triangular norms which accept fuzzy languages of infinite range and 4 a determinization algorithm for fuzzy automata its correctness proof and performance

inverse limits in category ltop ii this paper is devoted to the study of the inverse limits in ltop the category of l fuzzy topological spaces and continuous l valued zadeh functions between them where l is a completely distributive complete lattice structures of such limits are described and a series of their properties are investigated furthermore the mappings between two arbitrary inverse systems is defined and some of their properties are discussed for the case of category ltop

connectedness on fuzzy topological spaces in this paper properties of connectedness on completely distributive topological lattices definition 2 1 and fuzzy topological spaces 1 are studied some equivalent propositions on the concepts of functions in completely distributive lattices and connected elements in completely distributive lattices and fuzzy topological spaces are proved specially connectedness is characterized both by the r neighborhoods of molecules and c separations for any family li i i i of fuzzy topological spaces the product 1 is connected iff every li i is connected a continuous function maps connected elements onto connected ones the connectedness on the fuzzy real line r l is discussed in the last section as an important example the intervals defined here definition 4 1 must be connected in the fuzzy real line r l and so the intervals defined by rodabaugh in 13 are too any connected element is connected in the fuzzy real line r l if and only if r l r

weak bisimulations for fuzzy automata abstract forward and backward bisimulations have been introduced recently by ciric et al 2012 9 as a means for modeling the equivalence between states of fuzzy automata and approximating the language equivalence as well as for use in the state reduction of fuzzy automata the main aim of the present paper is to introduce two new kinds of bisimulations weak forward and backward bisimulations which provide better approximations of the language equivalence than forward and backward bisimulations and when employed in the state reduction they provide better reductions we give procedures for deciding whether there exist weak forward and backward simulations and bisimulations and for computing the greatest ones whenever they exist using weak bisimulations in conjunction with the concept of a uniform fuzzy relation we determine necessary and sufficient conditions under which two fuzzy automata are weak bisimulation equivalent we also characterize uniform weak backward and forward bisimulations between two fuzzy automata in terms of isomorphisms between their nerode and reverse nerode automata

computing behavior of finite fuzzy machines algorithm and its application to reduction and minimization we define finite fuzzy machines and investigate their behavior algorithm and software are proposed for computing behavior for establishing equivalence and redundancy of states and for solving reduction and minimization problems computational complexity of the algorithm is discussed testing examples are supplied the results are valid for finite max min min max and max product fuzzy machines

permanence in nonautonomous lotka volterra system with predator prey the nonautonomous lotka volterra system with m predators and n preys is considered in this paper average conditions are obtained for permanence and global attractivity in the system it is shown that our results are generalization of those of the periodic system

existence and global attractivity of positive periodic solutions for the impulsive delay nicholson s blowflies model in this paper we shall consider the following nonlinear impulsive delay population model 0 1 x t d t x t p t x t m w e a t x t m w a e t 0 t t k x t k 1 b k x t k k 1 2 where m is a positive integer d t a t and p t are positive periodic continuous functions with period w 0 in the nondelay case m 0 we show that 0 1 has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate linear periodic impulsive perturbations the impulsive delay equation 0 1 preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

characterizations of complete residuated lattice valued finite tree automata this paper deals with the concept of complete residuated lattice valued referred to as l valued finite tree automata in this regard we first define an l valued regular tree language and then we prove a necessary and sufficient condition for the regularity of an l valued tree language furthermore we generalize the pumping lemma for l valued finite tree automata l fta afterwards the behavior of l fta is addressed and some theorems are provided moreover the existence of the minimal form of an l fta is considered finally a minimization algorithm of the l fta is presented and its time complexity is analyzed

a comment on automata theory based on complete residuated lattice valued logic pushdown automata automata theory based on complete residuated lattice valued logic has been first established by qiu and then has been systematically studied by qiu and others the definition of l valued chomsky normal form in xing and qiu automata theory based on complete residuated lattice valued logic pushdown automata fuzzy sets and systems 160 2009 1125 1140 is somewhat different from that in xing and qiu pumping lemma in context free grammar theory based on complete residuated lattice valued logic fuzzy sets and systems 160 2009 1141 1151 in this note we give a more general l valued chomsky normal form to unify the two definitions we mainly show that for an l valued context free grammar an l valued greibach normal form can be equivalently constructed

minimization of fuzzy finite automata abstract in this paper we show that a fuzzy finite automation m 1 has an equivalent minimal fuzzy finite automation m we also show that m can be chsen so that if m 2 is equivalent to m 1 then m is a homomorphic image of m 2

on fuzzy regular languages abstract we introduce the concept of a max min fuzzy language fl m and a min max fuzzy language fl m recognized by a type of fuzzy automaton m we show that if l1 and l2 are finite valued f regular languages then so are l1 l2 and l1 l2 we give a form of a fuzzified pumping lemma which we use to give a necessary and sufficient condition for fl m to be nonconstant

asymptotic behaviors of competitive lotka volterra system with stage structure in this paper a two species competitive model with stage structure is presented and studied results on the global extinction and permanence are given which generalize the well known three theorems for the two species competitive system and moreover they confirm the negative effect of stage structure on the permanence of populations as well as estimate the degree of such effect conclusions in this paper suggest that for a competitive community stage structure is also one of the important reasons that cause permanence and extinction

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

equivalence reduction and minimization of finite fuzzy automata abstract a new algebraic approach to the problem of equivalence reduction and minimization of some kinds of fuzzy automata is given a system of necessary and sufficient conditions for equivalence of weakly initial fuzzy automata is formulated some algorithms considering the equivalence for two fuzzy automata are constructed

determinization of fuzzy automata with membership values in complete residuated lattices in this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices in comparison with the previous methods developed by belohlavek r belohlavek determinism and fuzzy automata information sciences 143 2002 205 209 and li and pedrycz y m li w pedrycz fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids fuzzy sets and systems 156 2005 68 92 our method always gives a smaller automaton and in some cases when the previous methods result in infinite automata our method can result in a finite one we also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them and in particular to the concept of the nerode s fuzzy right congruence of a fuzzy automaton which we introduce and study here

finite l fuzzy machines abstract for finite l fuzzy machines we develop behaviour reduction and minimization theory here l stands for l 0 1 where l is a totally ordered set with universal bounds 0 and 1 and the operations are join and meet the most essential results include investigating behaviour equivalence reduction and minimization problems and their algorithmical decidability

equivalence reduction and minimization of finite automata over semirings abstract a new unified approach to equivalence reduction and minimization of finite automata over semirings based on free semimodules is presented it includes as special cases deterministic nondeterministic stochastic and fuzzy automata a necessary and sufficient condition for the existence of a finite behaviour matrix for a given automaton is proved different algorithmical decidability properties for equivalence reduction and minimization are connected to a noetherian property in the category s mod c of the semimodules over the semiring c

on closure properties of l valued linear languages abstract in 2001 and 2002 daowen qiu has established a new theory of l valued automata which is based on complete residuated lattices moreover besides the finite automata several other classes of machines grammars and languages have been generalized using the ideas introduced by qiu this paper generalizes the concept of linear grammars and linear languages in this context moreover it presents some operations for l valued languages and some closure properties for the l valued linear languages

automata theory based on complete residuated lattice valued logic reduction and minimization automata theory based on complete residuated lattice valued logic called l valued finite automata l vfas has been established by qiu recently in this paper we define a kind of mealy type of l vfas mlfas a generalization of l vfas two kinds of statewise equivalence relations are introduced and a minimal form is defined we study the existence of the minimal form of an mlfa then we show that any two states can be distinguished by some word with finite length also a minimization algorithm of the mlfas is presented in addition we obtain a minimization algorithm for l vfas as well finally we define l valued languages l vls and l valued regular languages l vrls recognized by l vfas and provide some properties of l vrls

on the sum of l fuzzy topological spaces abstract h ghanim et al separation axioms subspaces and sums in fuzzy topology j math anal appl 102 1984 189 202 have extended the notion of sum for crisp topological spaces to fuzzy topological spaces and discussed the additivity for some fuzzy topological properties in this paper the concept of the sum of l fuzzy topological spaces is presented and its basic properties is discussed as the main results of the paper the additivity of separability and compactness in l fuzzy topological spaces is studied

separation properties of induced i l topological spaces the concept of induced i l topological spaces has been introduced by kubiak ph d thesis uam poznan 1985 and independently by wang kexue tongbao 34 5 1989 333 in this paper the separation properties in the sense of hutton reilly of induced i l topological spaces are investigated the main result of the paper is a characterization of l topological spaces by means of the appropriate hutton reilly separation properties of its induced i l topological space

pumping lemma in context free grammar theory based on complete residuated lattice valued logic residuated lattices are important algebras and have close links with various important algebras automata theory based on complete residuated lattice valued logic called l valued automata has been established by the second author in 2001 and 2002 as a continuation of automata theory based on complete residuated lattice valued logic in this paper we mainly deal with the problem concerning pumping lemma in l valued context free languages l cfls as a generalization of the notion in the theory of formal grammars the definition of l valued context free grammars l cfgs is introduced we also discuss a special case of l cfgs l right or left linear grammars and show the equivalence between l linear grammars and l regular grammars this result shows that we generalize the pumping lemma in l valued regular languages l rls more recently established by the second author

the effect of dispersal on permanence in a predator prey population growth model abstract in this paper we consider a periodic predator prey system where the prey can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation we assume a volterra within patch dynamic under the assumption that the average of dispersal rate from patch 1 to patch 2 is less than that of the intrinsic growth rate of prey in patch 1 we provide a sufficient and necessary condition to guarantee the prey and predator species to be permanent by using the main techniques in 1

equivalence in automata theory based on complete residuated lattice valued logic automata theory based on complete residuated lattice valued logic called l valued finite automata abbr l vfas was introduced by the second author in 2001 in this paper we deal with the problems of equivalence between l valued sequential machines abbr l vsms and l vfas we define l vsms and particularly present a method for deciding the equivalence between l vsms as well an algorithm procedure for deciding the equivalence between l vsms is constructed we analyze the complexity and efficiency of the algorithm procedure and obtain the relative results to l vfas moreover the definitions of l valued languages abbr l vls and l valued regular languages abbr l vrls recognized by l vfas are given and some related properties are also discussed we show an equivalent relation between l vrls and conventional regular languages by using l valued pumping lemma we get a necessary and sufficient condition for an l vl to be nonconstant

three dimensional periodic systems with trivial dynamics ii 3 where t g r u s u u u g v v r is open and f t u 1 2 3 f t u u f t u f t u u is continuous in v is t periodic in the i 1 2 2 3 2 3 time t and has continuous partial derivative fr u defined on r v we also assume that the following hypotheses hold h f r u f r u f r u and f r u 0 on r v 1 1 2 2 1 2 3 3 2 3 h f has a continuous extension f r v a r such that 2 0 0 f r u is defined and continuous in a neighborhood v of v 0 0

global dynamics of delay equations for populations with competition among immature individuals abstract we analyze a population model for two age structured species allowing for inter and intra specific competition at immature life stages the dynamics is governed by a system of delay differential equations ddes recently introduced by gourley and liu the analysis of this model presents serious difficulties because the right hand sides of the ddes depend on the solutions of a system of nonlinear odes and generally cannot be solved explicitly using the notion of strong attractor we reduce the study of the attracting properties of the equilibria of the ddes to the analysis of a related two dimensional discrete system then we combine some tools for monotone planar maps and planar competing lotka volterra systems to describe the dynamics of the model with three different birth rate functions we give easily verifiable conditions for global extinction of one or the two species and for global convergence of the positive solutions to a coexistence state

construction of fuzzy automata from fuzzy regular expressions li and pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice ordered monoid and generalize the well known results of the classical theory of formal languages in particular they have shown that a fuzzy language over an integral lattice ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton however they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression in this paper we provide such an efficient method transforming scalars appearing in a fuzzy regular expression ainto letters of the new extended alphabet we convert the fuzzy regular expression ato an ordinary regular expression a r then starting from an arbitrary nondeterministic finite automaton a that recognizes the language a r represented by the regular expression a r we construct fuzzy finite automata a a and a a r with the same or even less number of states than the automaton a which recognize the fuzzy language a represented by the fuzzy regular expression a the starting nondeterministic finite automaton a can be obtained from a r using any of the well known constructions for converting regular expressions to nondeterministic finite automata such as glushkov mcnaughton yamada s position automaton brzozowski s derivative automaton antimirov s partial derivative automaton or ilie yu s follow automaton

automata theory based on complete residuated lattice valued logic pushdown automata automata theory based on complete residuated lattice valued logic called l valued automata has been proposed by qiu automata theory based on complete residuated latticed valued logic sci china ser f 44 6 2001 419 429 automata theory based on complete residuated latticed valued logic ii sci china ser f 45 6 2002 442 452 in this paper we discuss some properties of l valued context free grammars languages and pushdown automata we show that for such grammars chomsky and greibach normal forms can be equivalently constructed and we also prove that the languages accepted by final states and by empty stack in l valued pushdown automata are equivalent in particular we prove the equivalence between l valued context free grammars and l valued pushdown automata

some categorical aspects of fuzzy topology research in recent years has revealed that the construct of fuzzy topological spaces behaves quite differently from that of topological spaces with respect to certain categorical properties in this paper we discuss some of these aspects since the topological construct l fts contains nontrivial both initially and finally closed full subconstructs and each such construct gives rise to a natural autonomous theory of fuzzy topology it can be said to some extent that fuzzy topology should consist of a system of closely related topology theories including the classical topology theory as a special case with each applying to one such subconstruct therefore in the first part of this paper the theory of sobriety is established for each finally and initially closed full subconstruct of l fts to illustrate this idea the second topic of this paper is the relationship between the construct of stratified l fuzzy topological spaces and several other familiar constructs in fuzzy topology for example the constructs of sostak fuzzy topological spaces and l fuzzifying topological spaces

theory of topological molecular lattices abstract the aim of this paper is to bring the theories of point set topology fuzzy topology and l fuzzy topology into a unified theory the theory of topological molecular lattices for this purpose we first introduce the concepts of molecule for completely distributive complete lattice molecular lattice for short the cotopology on it and the concept of remote neighborhoods of molecules therefrom we develop the theory of pointwise topology on molecular lattices

pumping lemma in automata theory based on complete residuated lattice valued logic a note abstract automata theory based on complete residuated lattice valued logic called l valued automata was established in qiu automata theory based on completed residuated lattice valued logic i science in china f 44 6 2001 419 429 qiu automata theory based on completed residuated lattice valued logic ii science in china f 45 6 2002 442 452 in this note we deal with the pumping lemma in l valued automata theory after recalling some preliminaries related to complete residuated lattices and l valued automata we define a number of l valued accepting predicates in particular the pumping lemma for l valued automata theory is set up we show that if those related l valued predicates are defined by using connective instead of then the pumping lemma may not hold again furthermore we investigate the l valued automata with e transitions and present the equivalence between the l valued automata without e transitions and those with e transitions finally a number of related questions is addressed

formal power series and regular operations on fuzzy languages in this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet and representation of fuzzy languages by these formal power series this representation generalizes the well known representation of fuzzy languages by their cut and kernel languages we show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages we use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series

some results on i l and r l abstract this paper gives a partial solution to problem 1 in wang and lu 1992 and a suggestion about how to construct a better fuzzy unit interval it defines a new kind of fuzzy real line and investigates a series of its properties

fuzzy language on free monoid in this paper we shall introduce the notion of fuzzy regular language adjunctive language and dense language and discuss their algebraic character and algebraic properties

fuzzy connectedness new definitions and comparisons abstract connectedness ultra f1 connectedness ultra f2 connectedness and strong f2 connectedness are defined for an arbitrary l subset their properties are studied and comparisons with some existing fuzzy connectedness notions such as strong f1 connectedness lowen s connectedness rodabaugh s connectedness zhao s connectedness etc are discussed in detail some standard examples of l topological spaces or l cotopological spaces which satisfy our new connectedness axioms are also given

connectedness in fuzzy topological spaces abstract we introduce four notions of connectedness for an arbitrary fuzzy set and discuss all the implications that exist between them using these notions various equivalence relations are defined on the set of fuzzy points components and quasi components are formed as the union of certain equivalence classes a fuzzy space is shown to be a dispoint union of its components in all the four cases and non overlapping union of its quasi components

extinction in periodic competitive stage structured lotka volterra model with the effects of toxic substances in this paper we consider a periodic competitive stage structured lotka volterra model with the effects of toxic substances it is shown that toxic substances play an important role in the extinction of species we obtain a set of sufficient conditions which guarantee that one of the components is driven to extinction while the other is globally attractive the numerical simulation of an example verifies our main results

permanence for a class of periodic time dependent competitive system with delays and dispersal in a patchy environment in this paper we study m species time delayed competitive lotka volterra type dispersal system with periodic coefficients in n patches by utilizing analytic method sufficient and realistic conditions on permanence and the existence of periodic solution are established the theoretical results are confirmed by a special example and numerical simulations

permanence and extinction in logistic and lotka volterra systems with diffusion abstract 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 differing from former studies our discussion includes the important situation in conservation biology in which species live in a weak patchy environment in the sense that species will become extinct in some of the isolated patches for the single population model we show that identical species can persist for some diffusion rates and can also vanish for another set of restrictions on the diffusion rates although the single endangered species will vanish in some isolated patches without contributions from other patches furthermore we consider the existence uniqueness and global stability of the positive periodic solution for prey predator systems we can make both the prey and the predator species permanent by choosing the diffusion rates appropriately even if the prey species has a negative intrinsic growth rate in some patches moreover we introduce an exotic competitive species y into the habitat occupied by the native species x competitive permanence and competitive exclusion both are considered the implications of these results are significant for the conservation of endangered species

permanence and asymptotic behavior of the n species nonautonomous lotka volterra competitive systems abstract in this paper we study the permanence and global asymptotic behavior for the n species nonautonomous lotka volterra competitive systems where all the parameters are time dependent and asymptotically approach periodic functions respectively some new criteria are established the corresponding results given by peng and chen in 1 are improved and extended

fuzzy topology fuzzy closure operator fuzzy compactness and fuzzy connectedness abstract in this paper definitions of fuzzy closure operator fuzzy compactness and fuzzy connectedness are given in a redefined fuzzy topological space and then some characteristic properties of fuzzy closure operator product theorems of fuzzy compactness invariance of fuzzy compactness and fuzzy connectedness under gradation preserving maps and invariance of fuzzy connectedness under the fuzzy closure operator are studied

stability of the boundary solution of a nonautonomous predator prey system with the beddington deangelis functional response abstract the dynamics of a nonautonomous predator prey system with the beddington deangelis functional response is studied from the perspective of extinction of the predator with the help of a fluctuation lemma we obtain a set of new sufficient conditions on the global asymptotic stability of the boundary solution which means the extinction of the predator the result not only improves but also complements some existing ones moreover the result indicates that the effect of the parameters is accumulative rather than pointwise

permanence extinction and periodic solution of predator prey system with beddington deangelis functional response in this paper we study permanence extinction and periodic solution of periodic predator prey system with beddington deangelis functional response we provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent in addition sufficient condition is derived for the existence of positive periodic solution this paper improves some main results obtained by fan and kuang m fan y kuang dynamics of nonautonomous predator prey system with the beddington deangelis functional response j math anal appl 295 2004 15 39

on the periodic lotka volterra competition model abstract we analyze the existence stability and multiplicity of t periodic coexistence states for the classical nonautonomous periodic lotka volterra competing species model this is done by treating the average values of the birth rates of species as parameters and studying the global structure of the set of coexistence states as these parameters vary as a result of this analysis we can explain the interesting differences between the results for the periodic case and the associated autonomous model

connectedness in l fuzzy topological spaces based on the consideration to the layer structures of fuzzy lattices and the level topologies of l fuzzy topological spaces a connectedness is defined for an arbitrary l fuzzy set in this paper this definition reflects the degree of connectivity of an l fuzzy set it is shown that the connectedness of l fuzzy topological spaces is an l good extension multiplicative and preserved under continuous l valued zadeh functions and that the inverse limit of continuums is a continuum general l fuzzy intervals and h intervals are defined and connectedness of them are proved it is also shown that the connectedness of an l fuzzy topological space is equivalent to the connectedness of its induced i l fuzzy topological space

higher separation axioms in l topologically generated i l topological spaces the main result of this paper is a theorem about inserting a pair of semicontinuous l real valued functions which extends the insertion theorem of kubiak comment math univ carolinae 34 1993 357 362 from l 0 1 to an arbitrary meet continuous lattice l endowed with an order reversing involution with this result it is shown that the normality type separation axioms in top l are preserved by the functor which takes an l topological space x to the i l topological space l x obtained by providing the set x with the i l topology consisting of all lower semicontinuous functions from x to i l the same is proved for the case of the regularity axiom

reduction of fuzzy automata by means of fuzzy quasi orders abstract in our recent paper we have established close relationships between state reduction of a fuzzy automaton and resolution of a particular system of fuzzy relation equations in that paper we have also studied reductions by means of those solutions which are fuzzy equivalences in this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi orders generally fuzzy quasi orders and fuzzy equivalences are equally good in the state reduction but we show that right and left invariant fuzzy quasi orders give better reductions than right and left invariant fuzzy equivalences we also show that alternate reductions by means of fuzzy quasi orders give better results than alternate reductions by means of fuzzy equivalences furthermore we study a more general type of fuzzy quasi orders weakly right and left invariant ones and we show that they are closely related to determinization of fuzzy automatons we also demonstrate some applications of weakly left invariant fuzzy quasi orders in conflict analysis of fuzzy discrete event systems

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

asymptotic classification of the positive solutions of the nonautonomous two competing species problem and assumed that the coefficients were continuous and periodic functions of the same period using a geometric analysis combined with the monotonicity properties of the solutions they obtained interesting consequences w x on the dynamics of this system one of the key results of 4 is theorem 4 8 this result partially describes the possible configurations of the attracting set of the semitrivial periodic solutions and is implicitly used several times throughout the paper in particular in theorems 5 4 and 5 9 w x while this result is correct the proof provided in 4 is somehow incomplete actually it assumes a priori that only certain configurations should be considered and does not look at a situation that at that moment of the proof cannot be disregarded see the remark to theorem 5 6 in our paper in the opinion of the present author the modifications required to complete the proof are nontrivial see proposition 5 4 and theorem 5 6 of our paper and this fact has motivated this paper in the process we obtain a full characterization of the attracting set of the semitrivial periodic solutions and a new formulation of the results that allows an extension to the nonperiodic case

bisimulations for fuzzy automata bisimulations have been widely used in many areas of computer science to model equivalence between various systems and to reduce the number of states of these systems whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata we prove that a uniform fuzzy relation between fuzzy automata a and b is a forward bisimulation if and only if its kernel and co kernel are forward bisimulation fuzzy equivalence relations on a and b and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalence relations as a consequence we get that fuzzy automata a and b are ufb equivalent i e there is a uniform forward bisimulation between them if and only if there is a special isomorphism between the factor fuzzy automata of a and b with respect to their greatest forward bisimulation fuzzy equivalence relations this result reduces the problem of testing ufb equivalence to the problem of testing isomorphism of fuzzy automata which is closely related to the well known graph isomorphism problem we prove some similar results for backward forward bisimulations and we point to fundamental differences because of the duality with the studied concepts backward and forward backward bisimulations are not considered separately finally we give a comprehensive overview of various concepts on deterministic nondeterministic fuzzy and weighted automata which are related to bisimulations

periodicity and stability for a lotka volterra type competition system with feedback controls and deviating arguments abstract this paper deals with the general periodic lotka volterra type competition systems with feedback controls and deviating arguments by employing fixed point index theory on cone an explicit necessary and sufficient condition for the global existence of the positive periodic solution of the systems is proved by constructing a suitable lyapunov functional a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution of the systems is given

myhill nerode type theory for fuzzy languages and automata the myhill nerode theory is a branch of the algebraic theory of languages and automata in which formal languages and deterministic automata are studied through right congruences and congruences on a free monoid in this paper we develop a general myhill nerode type theory for fuzzy languages with membership values in an arbitrary set with two distinguished elements 0 and 1 which are needed to take crisp languages in consideration we establish connections between extensionality of fuzzy languages w r t right congruences and congruences on a free monoid and recognition of fuzzy languages by deterministic automata and monoids and we prove the myhill nerode type theorem for fuzzy languages we also prove that each fuzzy language possess a minimal deterministic automaton recognizing it we give a construction of this automaton using the concept of a derivative automaton of a fuzzy language and we give a method for minimization of deterministic fuzzy recognizers in the second part of the paper we introduce and study nerode s and myhill s automata assigned to a fuzzy automaton with membership values in a complete residuated lattice the obtained results establish nice relationships between fuzzy languages fuzzy automata and deterministic automata

fuzzy path and fuzzy connectedness abstract this paper discusses fuzzy connectedness in fuzzy topology zadeh s classical paper 1 has introduced the fundamental concept of a fuzzy set upon which the foundation of fuzzy mathematics rests the theory of fuzzy topology is a branch of such mathematics our purpose is to introduce some basic concepts as fuzzy path fuzzy path connected set locally fuzzy path connected set in the fuzzy topological spaces and to prove some fundamental properties related to fuzzy connectedness

on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations in this paper we study systems of fuzzy relation inequalities and equations of the form u v i v i u i i where u is an unknown and v i i i are given fuzzy relations the dual systems v i u u v i i i their conjunctions the systems of the form u v i v i u i i and certain special types of these systems we call them weakly linear systems for each weakly linear system with a complete residuated lattice as the underlying structure of truth values we prove the existence of the greatest solution and we provide an algorithm for computing the greatest solution which works whenever the underlying complete residuated lattice is locally finite otherwise we determine some sufficient conditions under which the algorithm works the algorithm is iterative and each its single step can be viewed as solving of a particular linear system weakly linear systems emerged from the fuzzy automata theory but we show that they also have important applications in other fields e g in the concurrency theory and social network analysis

population systems with nonlinear discrete diffusion terms where fi gi r r r are continuous functions which are t periodic in t and locally lipschitz continuous in xi yi and d d1 dn e e1 en are t periodic nonlinear diffusion functions in the sense of 9 that is d t x e t x are positive homogeneous in x cooperative and irreducible 9 as usual xi yi represent the population density of the species at the patch i we will assume that

average growth and extinction in a competitive lotka volterra system abstract in this paper we answer an earlier conjecture consider a class of nonautonomous competitive lotka volterra systems we show that certain inequalities involving the interaction coefficients and averages of the growth rates imply that the system is persistent however reversing one of these inequalities implies that the n th species goes to extinction

automata theory based on complete residuated lattice valued logic a categorical approach automata theory based on complete residuated lattice valued logic called l valued automata l vas has been primarily established by qiu in 2001 and 2002 in this paper we consider the l vas that have l valued initial and final states we study the categorical issue of l vas the main technical contributions include 1 we investigate the relationship between the category of l vas and the category of non deterministic automata ndas also we study the relationship between the category of generalized l vas and the category of ndas 2 we prove the existence of isomorphisms between the category of l vas and the subcategory of generalized l vas and between the category of l vas and the category of sets of ndas 3 finally we further investigate some specific relationships between the output l valued subsets of generalized l vas and the output l valued subsets of ndas

computation of the greatest simulations and bisimulations between fuzzy automata recently two types of simulations forward and backward simulations and four types of bisimulations forward backward forward backward and backward forward bisimulations between fuzzy automata have been introduced if there is at least one simulation bisimulation of some of these types between the given fuzzy automata it has been proved that there is the greatest simulation bisimulation of this kind in the present paper for any of the above mentioned types of simulations bisimulations we provide an efficient algorithm for deciding whether there is a simulation bisimulation of this type between the given fuzzy automata and for computing the greatest one whenever it exists the algorithms are based on the method developed in ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 which comes down to the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations

extinction and permanence in nonautonomous competitive system with stage structure in this paper the n species nonautonomous stage structured competitive system is constructed and considered sufficient conditions for its extinction and permanence are obtained results here generalize and unify some previous ones moreover it is concluded that stage structure in this system is one of the important factors that effect the extinction and permanence of species

survey of local connectedness axioms and their properties in l topological spaces based on the notions of fuzzy connectedness defined by lu and li fuzzy connectedness new definitions and comparisons fuzzy sets and systems 157 2006 1928 1940 some new fuzzy local connectedness such as local connectedness local ultra f 1 connectedness local strong f 1 connectedness local ultra f 2 connectedness local strong f 2 connectedness ultra f 1 local connectedness strong f 1 local connectedness ultra f 2 local connectedness and strong f 2 local connectedness of l topological spaces or l cotopological spaces are defined in this paper apart from maintaining some frequently used properties that classical local connected topological spaces possess l topological spaces or l cotopological spaces which satisfy our new fuzzy local connectedness axioms also have some interesting properties for example local connectedness local ultra f 1 connectedness local ultra f 2 connectedness local strong f 1 connectedness and local strong f 2 connectedness are all i l inducible if l is a complete and meet continuous demorgan algebra they are l extension of local connectedness of topological spaces under some moderate restrictions to l it is proved that all l intervals are locally connected if copr l is a generating set of l some categorical results reflecting the differences between classical topology and l topology are obtained the relationships between these notions of connectedness are also investigated in detail

local connectedness in l topological spaces this paper studies local strong f1 connectedness and local q connectedness of l topological spaces it is shown that every l interval j l and its weak inducification j l are both local strong f1 connected and local q connected and that the local q connectedness of an l topological space is equivalent to that of its induced i l topological space

time delayed parabolic system in a two species competitive model with stage structure a two species competitive model with stage structure is discussed the dynamics of coupled system of semilinear parabolic equations with time delays are investigated results on the local and global stabilities of the axial equilibria and positive equilibrium are given our results show that the introduction of diffusion does not affect the permanence and extinction of the species though the introduction of stage structure brings negative effect on it