a new method for complete stability analysis of cellular neural networks with time delay this paper presents new complete stability results for delayed cellular neural networks dcnns a novel method is proposed for complete stability analysis of dcnns by applying the m matrix theory and introducing some new estimation techniques on the solutions of dcnns a simple and improved complete stability criterion is derived the new criterion unifies the delay dependent and delay independent complete stability conditions for dcnns moreover the obtained delay dependent criterion can give a larger upper bound of the time delay than the existing ones such that the complete stability can still be retained numerical examples are presented which show that the new complete stability results for dcnns are compared favorably with the existing results

adaptive fuzzy tracking control for a class of pure feedback nonlinear systems with time varying delay and unknown dead zone abstract this paper investigates the problem of adaptive fuzzy tracking control for a category of pure feedback nonlinear systems with time varying delay and unknown dead zone fuzzy logic systems are used to identify unknown functions existing in systems mean value theorem is introduced to overcome the difficulty arising from the pure feedback structure in designing controller based on the information of dead zone slopes dead zone is handled only one adaptive parameter needs updating online by considering the norm of membership function vectors rather than all sub vectors moreover utilizing the adaptive backstepping technique a novel adaptive fuzzy tracking control scheme is developed to guarantee all signals of the closed loop systems are semi globally uniformly ultimately bounded and the tracking error can be regulated to the origin with a small neighborhood the stability of the closed loop system is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach

a new framework for multivariate general conformable fractional calculus and potential applications abstract some applications of fractional partial differential equations fpdes based on conformable fractional derivative cfd are discussed recently as an extension of cfd power kernel is generalized to other normalized probability distribution kernels general conformable fractional derivative gcfd provides a framework to explain the physical meaning of cfd and describe which phenomena or processes gcfd cfd are suitable to model we will establish the multivariate theory of gcfd in this paper compared with traditional hereditary fractional calculus like riemann liouville type or caputo type the unified theory of gcfd vector calculus has well forms with simplicity and elegance as applications fractional maxwell s equations of gcfd are given to describe electromagnetic fields of media that demonstrate inhomogeneous complicated and local properties and some fractional parabolic equations are presented as natural extensions of some nonlinear parabolic equations that cover several important famous equations

relaxed conditions for stability of time varying delay systems in this paper the problem of delay dependent stability analysis of time varying delay systems is investigated firstly a new inequality which is the modified version of free matrix based integral inequality is derived and then by aid of this new inequality two novel lemmas which are relaxed conditions for some matrices in a lyapunov function are proposed based on the lemmas improved delay dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality lmi two numerical examples are given to describe the less conservatism of the proposed methods

an improved global asymptotic stability criterion for delayed cellular neural networks a new lyapunov krasovskii functional is constructed for delayed cellular neural networks and the s procedure is employed to handle the nonlinearities an improved global asymptotic stability criterion is also derived that is a generalization of and an improvement over previous results numerical examples demonstrate the effectiveness of the criterion

constructing and predicting solitary pattern solutions for nonlinear time fractional dispersive partial differential equations building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics physics and engineering in this work a new analytical technique for constructing and predicting solitary pattern solutions of time fractional dispersive partial differential equations is proposed based on the generalized taylor series formula and residual error function the new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software for method evaluation and validation the proposed technique was applied to three different models and compared with some of the well known methods the resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct as well as the prediction of solitary pattern solutions for time fractional dispersive partial differential equations

variational iteration method and homotopy perturbation method for nonlinear evolution equations he s variational iteration and homotopy perturbation methods are applied to various evolution equations to assess the accuracy of the solutions we compare the results with the exact solutions revealing that both methods are capable of solving effectively a large number of nonlinear differential equations with high accuracy

conformable derivative approach to anomalous diffusion abstract by using a new derivative with fractional order referred to conformable derivative an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion the analytical solutions of the conformable derivative model in terms of gauss kernel and error function are presented the power law of the mean square displacement for the conformable diffusion model is studied invoking the time dependent gauss kernel the parameters related to the conformable derivative model are determined by levenberg marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete the data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation furthermore the potential application of the proposed conformable derivative model of water flow in low permeability media is discussed

mixed h l2 l state estimation for switched genetic regulatory networks subject to packet dropouts a persistent dwell time switching mechanism abstract in this work a kind of switched gene regulatory networks with packet dropout and uncertainties are constructed by switched coupled nonlinear difference equations in comparison a more comprehensive switching regulation persistent dwell time is employed to it the aim is to construct a mixed mode dependent and mode independent estimator for the before mentioned gene regulatory networks with a view to the loss of system modal information thereafter the augmented system is established after that the sufficient conditions of the exponential stability and mixed h l 2 l performance for the augmented system are deduced by the switching lyapunov theory finally a numerical example is employed to elucidate the validity of the estimator gains decoupled by the congruent transformation

a kam theorem for hamiltonian partial differential equations with unbounded perturbations we establish an abstract infinite dimensional kam theorem dealing with unbounded perturbation vector field which could be applied to a large class of hamiltonian pdes containing the derivative x in the perturbation especially in this range of application lie a class of derivative nonlinear schrodinger equations with dirichlet boundary conditions and perturbed benjamin ono equation with periodic boundary conditions so kam tori and thus quasi periodic solutions are obtained for them

new stability results for delayed neural networks this paper is concerned with the stability for delayed neural networks by more fully making use of the information of the activation function a new lyapunov krasovskii functional lkf is constructed then a new integral inequality is developed and more information of the activation function is taken into account when the derivative of the lkf is estimated by lyapunov stability theory a new stability result is obtained finally three examples are given to illustrate the stability result is less conservative than some recently reported ones

delay dependent global exponential stability for delayed recurrent neural networks this paper deals with the global exponential stability for delayed recurrent neural networks drnns by constructing an augmented lyapunov krasovskii functional and adopting the reciprocally convex combination approach and wirtinger based integral inequality delay dependent global exponential stability criteria are derived in terms of linear matrix inequalities meanwhile a general and effective method on global exponential stability analysis for drnns is given through a lemma where the exponential convergence rate can be estimated with this lemma some global asymptotic stability criteria of drnns acquired in previous studies can be generalized to global exponential stability ones finally a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results

invariant cantor manifolds of quasi periodic oscillations for a nonlinear schrodinger equation this paper was written while both authors were guests of the forschungsinstitut fur mathematik at the eth zurich and we thank the institute for its hospitality pleasant working atmosphere and helpful staff in particular we thank jiirgen moser for numerous stimulating discussions on the subject we also benefitted from a remark by sigurd angenent concerning the analyticity of the solutions the second author also thanks the deutsche forschungsgemeinschaft for their financial support through a heisenberg grant

quasi periodic solutions for perturbed autonomous delay differential equations abstract this work discusses the persistence of quasi periodic solutions for delay differential equations we prove that the perturbed system possesses a quasi periodic solution under appropriate hypotheses if an unperturbed linear system has quasi periodic solutions we extend some well known results on ordinary differential equations to delay differential equations

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

the relation between the size of perturbations and the dimension of tori in an infinite dimensional kam theorem of poschel abstract in this paper we discuss the relation between the size of perturbations and the dimension of tori based on the kam theorem of poschel 1996 which can be applied to infinite dimensional pdes in other words we give a quantitative version of the kam theorem of poschel 1996 moreover motivated by chung and yuan 2007 2008 and li and yuan 2012 after infinite kam iterations we make action and normal variables of kam tori of the reduced hamiltonian system in a domain instead of shrinking them to the origin

an analytic study of fisher s equation by using adomian decomposition method in this paper we develop a framework to obtain exact solutions to fisher s equation and to a nonlinear diffusion equation of the fisher type by employing adomian decomposition method the proposed scheme is supported by examining nonlinear diffusion equations of the fisher type

further result on asymptotic stability criterion of cellular neural networks with time varying discrete and distributed delays based on a recent work and the linear matrix inequality lmi optimization approach we extend the recent work on global asymptotic stability of a class of neural networks to uncertain cellular neural networks with time varying discrete and distributed delays

approximate analytical solution of the nonlinear fractional kdv burgers equation in this paper explicit and approximate solutions of the nonlinear fractional kdv burgers equation with time space fractional derivatives are presented and discussed the solutions of our equation are calculated in the form of rabidly convergent series with easily computable components the utilized method is a numerical technique based on the generalized taylor series formula which constructs an analytical solution in the form of a convergent series five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution the results reveal that the method is very effective and simple in determination of solution of the fractional kdv burgers equation

robust stability analysis for stochastic neural networks with time varying delay this brief investigates the problem of mean square exponential stability of uncertain stochastic delayed neural networks dnns with time varying delay a novel lyapunov functional is introduced with the idea of the discretized lyapunov krasovskii functional lkf method then a new delay dependent mean square exponential stability criterion is derived by applying the free weighting matrix technique and by equivalently eliminating time varying delay through the idea of convex combination numerical examples illustrate the effectiveness of the proposed method and the improvement over some existing methods

periodic and quasi periodic solutions of nonlinear wave equations via kam theory in this paper the nonlinear wave equation u u u xx v x u x t varepsilon u 3 x t 0 is studied it is shown that for a large class of potentials v x one can use kam methods to construct periodic and quasi periodic solutions in time for this equation

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

estimation of domain of attraction for aperiodic sampled data switched delayed neural networks subject to actuator saturation in this paper for the case of the asynchronous switching caused by that subsystem s switching occuring during a sampling interval the domain of attraction estimation problem is investigated for aperiodic sampled data switched delayed neural networks asdsdnns subject to actuator saturation a parameters dependent time scheduled lyapunov functional consisting of a novel looped functional is constructed using segmentation technology and linear interpolation by employing this novel functional and using an average dwell time adt approach exponential stability criteria are proposed for polytopic uncertain asdsdnns subject to actuator saturation and a relationship between adt and sampling period is revealed for asdsdnns as a corollary exponential stability criteria are proposed for nominal asdsdnns subject to actuator saturation furthermore by describing the domain of attraction as a time varying ellipsoid determined by the time scheduled lyapunov matrix the proposed theoretical conditions are transformed into a linear matrix inequality lmi based multi objective optimization problem the dynamic estimates of the domain of attraction for asdsdnns are solved numerical simulation examples are provided to illustrate the effectiveness of the proposed method

admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays this paper is concerned with global asymptotic stability of a neural network with a time varying delay where the delay function is differentiable uniformly bounded with delay derivative bounded from above first a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions this inequality provides a tighter bound in the form of a convex combination than some existing ones second by constructing proper lyapunov krasovskii functional global asymptotic stability of the neural network is analyzed for two types of the time varying delays depending on whether or not the lower bound of the delay derivative is known third noticing that sufficient conditions on stability from estimation on the derivative of some lyapunov krasovskii functional are affine both on the delay function and its derivative allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study finally two numerical examples are given to substantiate the effectiveness of the proposed method

on the persistence of quasi periodic invariant tori for double hopf bifurcation of vector fields abstract we analyze the persistence of quasi periodic invariant 2 and 3 tori for the double hopf hopf hopf bifurcation by using the kam method we prove that in a sufficiently small neighborhood of the bifurcation point the full system has quasi periodic 2 tori for most of the parameter sets where its truncated normal form possesses 2 tori under appropriate conditions we obtain that the full system also has quasi periodic 3 tori for most parameters near the hopf bifurcation curve of its truncated normal form and along the direction of the bifurcation and these 3 tori bifurcate from invariant 2 tori we also give concrete formulas on the existence of quasi periodic invariant 2 and 3 tori which are based on coefficients of the truncated normal form

global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays by employing the lyapunov krasovskii functional and linear matrix inequality lmi approach the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time varying delays and distributed time varying delays some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time varying delay the proposed lmi result is computationally efficient as it can be solved numerically using standard commercial software two examples are given to show the usefulness of the results

existence and stability of quasi periodic breathers in networks of ginzburg landau oscillators abstract it is shown that there is an attracting quasi periodic breather in networks of ginzburg landau oscillators

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

complete delay decomposing approach to asymptotic stability for neural networks with time varying delays this paper is concerned with the problem of stability of neural networks with time varying delays a novel lyapunov krasovskii functional decomposing the delays in all integral terms is proposed by exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals some new generalized delay dependent stability criteria are established which are different from the existing ones and improve upon previous results numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method

stability analysis of distributed delay neural networks based on relaxed lyapunov krasovskii functionals this paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays the distributed delays are assumed to be constant and prescribed since a positive definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite it is important for constructing relaxed lyapunov krasovskii functionals which generally lead to less conservative stability criteria based on this fact and using two kinds of integral inequalities a new delay dependent condition is obtained which ensures that the distributed delay neural network under consideration is globally asymptotically stable this stability criterion is then improved by applying the delay partitioning technique two numerical examples are provided to demonstrate the advantage of the presented stability criteria

some remarks on the use of time varying delay to model sample and hold circuits this note revises the so called input delay approach to the control of sampled data systems with nonuniform sampling in which the sample and hold circuit is embedded into an analog system with a time varying input delay it is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57 if the time varying delay embedding step is omitted

branching of cantor manifolds of elliptic tori and applications to pdes we consider infinite dimensional hamiltonian systems we prove the existence of cantor manifolds of elliptic tori of any finite higher dimension accumulating on a given elliptic kam torus then close to an elliptic equilibrium we show the existence of cantor manifolds of elliptic tori which are branching points of other cantor manifolds of higher dimensional tori we also answer to a conjecture of bourgain proving the existence of invariant elliptic tori with tangential frequency along a pre assigned direction the proofs are based on an improved kam theorem its main advantages are an explicit characterization of the cantor set of parameters and weaker smallness conditions on the perturbation we apply these results to the nonlinear wave equation

further results on delay dependent stability criteria of neural networks with time varying delays in this brief paper an augmented lyapunov functional which takes an integral term of state vector into account is introduced owing to the functional an improved delay dependent asymptotic stability criterion for delayed neural networks nns is derived in term of linear matrix inequalities lmis it is shown that the obtained criterion can provide less conservative result than some existing ones when linear fractional uncertainties appear in nns a new robust delay dependent stability condition is also given numerical examples are given to demonstrate the applicability of the proposed approach

revisited fisher s equation in a new outlook a fractional derivative approach abstract the well known fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system the modified model is analyzed both analytically and numerically a comparatively new technique residual power series method is used for finding approximate solutions of the modified fisher model a new technique combining sinc collocation and finite difference method is used for numerical study the abundance of the bird species phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters we conjecture non diffusive and diffusive fractional fisher equation represents the same dynamics in the interval memory index 0 8384 0 9986 we also observe that when the value of memory index is close to zero the solutions bifurcate and produce a wave like pattern we conclude that the survivability of the species increases for long range memory index these findings are similar to fisher observation and act in a similar fashion that advantageous genes do

cost effective robust stabilization and bifurcation suppression a novel technique of robust stabilization and bifurcation suppression is proposed the proposed method the center probe method stabilizes an equilibrium point of a delay differential equation at

hierarchical stability conditions for a class of generalized neural networks with multiple discrete and distributed delays this brief investigates the analysis issue for global asymptotic stability of a class of generalized neural networks with multiple discrete and distributed delays to tackle delays arising in different neuron activation functions we employ a generalized model with multiple discrete and distributed delays which covers various existing neural networks we then generalize the bessel legendre inequalities to deal with integral terms with any linearly independent functions and nonlinear function of states based on these inequalities we design the lyapunov krasovskii functional and derive hierarchical linear matrix inequality stability conditions finally three numerical examples are provided to demonstrate that the proposed method is less conservative with a reasonable numerical burden than the existing results

modified simple equation method for nonlinear evolution equations abstract this paper reflects the implementation of a reliable technique which is called modified simple equation method msem for solving evolution equations the proposed algorithm has been successfully tested on two very important evolution equations namely fitzhugh nagumo equation and sharma tasso olver equation numerical results are very encouraging

lmi based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying lebesgue stieljies measures on the basis of linear matrix inequality the concerned network model includes many neural network models with various delays and structures as its special cases such as the delays covering the discrete delays and distributed delays and the network structures containing the neutral type networks and high order networks therefore many new stability criteria for the above neural network models have also been derived from the present stability analysis method all the obtained stability results have similar matrix inequality structures and can be easily checked three numerical examples are used to show the effectiveness of the obtained results

fault detection for discrete time linear systems based on descriptor observer approach this paper investigates the problem of actuator fault detection filter design for discrete time linear systems with output disturbance by using the descriptor observer method an h fault detection filter is designed to guarantee the residual system is admissible and satisfies the h performance by utilizing lyapunov function approach a sufficient condition for the admissible of the residual system is obtained in the form of linear matrix inequality lmi the desired fault detection filter can be designed by solving a set of lmis finally a numerical example is proposed to illustrate the effectiveness of the developed method

stability analysis for delayed neural networks with an improved general free matrix based integral inequality this paper revisits the problem of stability analysis for neural networks with a time varying delay an improved general free matrix based fmb integral inequality is proposed with an undetermined number m compared with the conventional fmb ones the improved inequality involves a much smaller number of free matrix variables in particular the improved fmb integral inequality is expressed in a concrete form for any value of m by employing the new inequality with a properly constructed lyapunov krasovskii functional a new stability condition is derived for neural networks with a time varying delay two commonly used numerical examples are given to show strong competitiveness of the proposed approach in both the conservatism and computation burdens

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays this paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays a sufficient condition which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient is established in terms of the linear matrix inequality lmi technique and a new lyapunov krasovskii functional the estimating procedure is implemented by solving a set of lmis which can be checked easily by effective algorithms under the proposed condition the algebraic subsystems possess the same decay rate as the differential ones moreover a state feedback stabilizing controller which makes the closed loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed numerical examples are provided to illustrate the effectiveness of the theoretical results

a new criterion of delay dependent asymptotic stability for hopfield neural networks with time delay in this brief the problem of global asymptotic stability for delayed hopfield neural networks hnns is investigated a new criterion of asymptotic stability is derived by introducing a new kind of lyapunov krasovskii functional and is formulated in terms of a linear matrix inequality lmi which can be readily solved via standard software this new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning an example is provided to show the effectiveness and the advantage of the proposed result

improved delay dependent asymptotic stability criteria for delayed neural networks this brief is concerned with asymptotic stability of neural networks with uncertain delays two types of uncertain delays are considered one is constant while the other is time varying the discretized lyapunov krasovskii functional lkf method is integrated with the technique of introducing the free weighting matrix between the terms of the leibniz newton formula the integrated method leads to the establishment of new delay dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks dnns a numerical simulation study is conducted to demonstrate the obtained theoretical results which shows their less conservatism than the existing stability criteria

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

a new modification of adomian decomposition method for solving a kind of evolution equation in this paper we propose a new modification of adomian decomposition method for solving a kind of evolution equation the modification will improve the convergence of the series solution the validity of the modified technique is verified through illustrative examples

finite time state estimation for coupled markovian neural networks with sensor nonlinearities this paper investigates the issue of finite time state estimation for coupled markovian neural networks subject to sensor nonlinearities where the markov chain with partially unknown transition probabilities is considered a luenberger type state estimator is proposed based on incomplete measurements and the estimation error system is derived by using the kronecker product by using the lyapunov method sufficient conditions are established which guarantee that the estimation error system is stochastically finite time bounded and stochastically finite time stable respectively then the estimator gains are obtained via solving a set of coupled linear matrix inequalities finally a numerical example is given to illustrate the effectiveness of the proposed new design method

stability and dissipativity analysis of distributed delay cellular neural networks in this brief the problems of delay dependent stability analysis and strict q s dissipativity analysis are investigated for cellular neural networks cnns with distributed delay first by introducing an integral partitioning technique two new forms of lyapunov krasovskii functionals are constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities based on this criterion a new sufficient delay and dependent condition is given to guarantee that the cnns with distributed delay are strictly q s dissipative the results developed in this brief can tolerate larger allowable delay than existing ones in the literature which is demonstrated by several examples

kam for the nonlinear schrodinger equation we consider the d dimensional nonlinear schrodinger equation under periodic boundary conditions i dot u delta u v x u ep frac p f p bar u x u bar u quad u u t x x in t d where v x sum hat v a e i sc a x is an analytic function with hat v real and f is a real analytic function in re u im u and x this equation is a popular model for the real nls equation where instead of the convolution term v u we have the potential term vu for ep 0 the equation is linear and has time quasi periodic solutions u u t x sum a in a hat u a e i a 2 hat v a t e i sc a x quad hat u a 0 where a is any finite subset of z d we shall treat omega a a 2 hat v a a ina as free parameters in some domain u subset r a this is a hamiltonian system in infinite degrees of freedom degenerate but with external parameters and we shall describe a kam theory which under general conditions will have the following consequence if ep is sufficiently small then there is a large subset u of u such that for all omega in u the solution u persists as a time quasi periodic solution which has all lyapounov exponents equal to zero and whose linearized equation is reducible to constant coefficients

stability analysis of quaternion valued neural networks with both discrete and distributed delays abstract the existence uniqueness and stability of the equilibrium of quaternion valued neural networks qvnns with both discrete and distributed delays are investigated in this paper the considered model is managed as a single entirety without decomposition based on homeomorphic mapping theorem and linear matrix inequality several sufficient criteria are derived to ascertain the aforementioned qvnns to be globally asymptotically stable and exponentially stable moreover provided criteria can be verified by the linear matrix inequality lmi toolbox in matlab finally one simulation example is demonstrated to verify the effectiveness of obtained results

global asymptotic stability for a class of generalized neural networks with interval time varying delays this paper is concerned with global asymptotic stability for a class of generalized neural networks nns with interval time varying delays which include two classes of fundamental nns i e static neural networks snns and local field neural networks lfnns as their special cases some novel delay independent and delay dependent stability criteria are derived these stability criteria are applicable not only to snns but also to lfnns it is theoretically proven that these stability criteria are more effective than some existing ones either for snns or for lfnns which is confirmed by some numerical examples

a new definition of fractional derivative we give a new definition of fractional derivative and fractional integral the form of the definition shows that it is the most natural definition and the most fruitful one the definition for email protected email protected 1 coincides with the classical definitions on polynomials up to a constant further if a 1 the definition coincides with the classical definition of first derivative we give some applications to fractional differential equations

the residual power series method for the one dimensional unsteady flow of a van der waals gas abstract a residual power series scheme is developed for mixed type p system of conservation laws the residual power series method rpsm does not require discretization reduces the system to an explicit system of algebraic equations and consequently of massive computations convergence hypotheses are discussed and error bounds of exponential rates are derived the scheme is numerically tested to several cases of the van der waals equations which arise in fluid dynamics stability is obtained graphically while transition through regions the reported results reveal the reliability efficiency and economical implementation of the proposed algorithm for handling nonlinear partial differential equations in applied mathematics

new passivity analysis for neural networks with discrete and distributed delays in this brief the problem of passivity analysis is investigated for a class of uncertain neural networks nns with both discrete and distributed time varying delays by constructing a novel lyapunov functional and utilizing some advanced techniques new delay dependent passivity criteria are established to guarantee the passivity performance of nns essentially different from the available results when estimating the upper bound of the derivative of lyapunov functionals we consider and best utilize the additional useful terms about the distributed delays which leads to less conservative results these criteria are expressed in the form of convex optimization problems which can be efficiently solved via standard numerical software numerical examples are provided to illustrate the effectiveness and less conservatism of the proposed results

recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation abstract nonlinear evolution equations nees are very important partial differential equations in nonlinear physics optics and engineering in this article we apply the residual power series rps method to the initial value problem of the nonlinear spatial conformable fractional evolution equations coefficients of the analytic solution are computed by recursive formulae and the famous nonlinear spatial conformable fractional fisher equation is taken as an example to verify this method direct computations demonstrate the correctness of the recursive formulae meanwhile the recursive formulae can be easily implemented by mathematical software

producing stable periodic solutions of switched impulsive delayed neural networks using a matrix based cubic convex combination approach this article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time varying delays first tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks second a sufficient criterion for the existence uniqueness and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse delay dependent lyapunov krasovskii functional method it is worth emphasizing that the addressed lyapunov krasovskii functional covers both triple integral terms and novel quadruple integral terms which makes the conservatism of the above criteria decrease even if the original neural network models are unstable or the impulsive effects are strong the addressed neural network model can produce a globally exponentially stable periodic solution these results here which include boundedness globally uniformly exponential convergence and globally exponentially stability of the periodic solution generalize and improve the earlier publications finally two numerical examples and their computer simulations are given to show the effectiveness of theoretical results

analytic study on two nonlinear evolution equations by using the g g expansion method abstract the validity and reliability of the so called g g expansion method is tested by applying it to two nonlinear evolutionary equations solutions in more general forms are obtained when the parameters are taken as special values it is observed that the previously known solutions can be recovered new rational function solutions are also presented being concise and less restrictive the method can be applied to many nonlinear partial differential equations

h state estimation for neural networks with general activation function and mixed time varying delays this article deals with h state estimation of neural networks with mixed delays in order to make full use of delay information novel delay product lyapunov krasovskii functional lkf by using parameterized delay interval is first constructed then generalized free weighting matrix integral inequality is used to estimate the derivative of lkf to reduce the conservatism also a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model finally sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed h performance numerical examples are simulated to show the benefits of our proposed method