numerical solutions of variable order time fractional 1 1 and 1 2 dimensional advection dispersion and diffusion models abstract a numerical scheme based on haar wavelets coupled with finite differences is suggested to study variable order time fractional partial differential equations tfpdes the technique is tested on 1 1 dimensional advection dispersion and 1 2 dimensional advection diffusion equations in the proposed scheme time fractional derivative is firstly approximated by quadrature formula and then finite differences are combined with one and two dimensional haar wavelets with the help of suggested method the tfpdes convert to a system of algebraic equations which is easily solvable also convergence of the proposed scheme has been discussed which is an important part of the present work for validation the obtained results are matched with earlier work and exact solutions computations illustrate that the proposed scheme has better outcomes

a rbf based differential quadrature method for solving two dimensional variable order time fractional advection diffusion equation abstract numerical simulation technique of two dimensional variable order time fractional advection diffusion equation is developed in this paper using radial basis function based differential quadrature method rbf dq to the best of the authors knowledge this is the first application of this method to variable order time fractional advection diffusion equations for the general case of irregular geometries the meshless local form of rbf dq is used and the multiquadric type of radial basis functions is selected for the computations this approach allows one to define a reconstruction of the local radial basis functions to treat accurately both the dirichlet and neumann boundary conditions on the irregular boundaries the method is validated by the well documented test examples involving variable order fractional modeling of air pollution the numerical results demonstrate that the proposed method provides accurate solutions for two dimensional variable order time fractional advection diffusion equations

existence stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations abstract in this paper we study the existence stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise we first prove the existence and uniqueness of tempered random attractors for the stochastic equations and characterize the structures of the attractors by random complete solutions we then examine the existence and stability of random complete quasi solutions and establish the relations of these solutions and the structures of tempered attractors when the stochastic equations are incorporated with periodic forcing we obtain the existence and stability of random periodic solutions for the stochastic chafee infante equation we further establish the multiplicity and stochastic bifurcation of complete and periodic solutions

global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type in this paper by using the lyapunov krasovskii functional method we investigate the global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type some new stability criteria are presented in terms of linear matrix inequality lmi two numerical examples are also given to show the effectiveness of the obtained results using lmi control toolbox in matlab

mean square global asymptotic stability of stochastic recurrent neural networks with distributed delays by constructing suitable lyapunov functionals and combining with matrix inequality technique a new simple sufficient condition is presented for the global asymptotic stability in the mean square of delayed neural networks

mean square exponential stability of stochastic recurrent neural networks with time varying delays the stability of a class of stochastic recurrent neural networks with time varying delays is investigated in this paper with the help of the lyapunov function and the dini derivative of the expectation of v t x t along the solution x t of the model a set of novel sufficient conditions on mean square exponential stability has been established an example is also given to illustrate the effectiveness of our results

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

a meshless method for solving two dimensional variable order time fractional advectiondiffusion equation several physical phenomena such as transformation of pollutants energy particles and many others can be described by the well known convectiondiffusion equation which is a combination of the diffusion and advection equations in this paper this equation is generalized with the concept of variable order fractional derivatives the generalized equation is called variable order time fractional advectiondiffusion equation v otfade an accurate and robust meshless method based on the moving least squares mls approximation and the finite difference scheme is proposed for its numerical solution on two dimensional 2 d arbitrary domains in the time domain the finite difference technique with a weighted scheme and in the space domain the mls approximation are employed to obtain appropriate semi discrete solutions since the newly developed method is a meshless approach it does not require any background mesh structure to obtain semi discrete solutions of the problem under consideration and the numerical solutions are constructed entirely based on a set of scattered nodes the proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere in all such cases the obtained results show that the proposed method is very accurate and robust moreover a remarkable property so called positive scheme for the proposed method is observed in solving concentration transport phenomena the variable order time fractional advectiondiffusion equation in 2 d is defined an accurate and robust meshless method is proposed for its numerical solutions a variable order fractional modeling of air pollution is expressed and investigated it is shown that the proposed method is a positive scheme the proposed method can be extended for other types of variable order fractional problems

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

global asymptotic stability of stochastic cohen grossberg type bam neural networks with mixed delays an lmi approach in this paper we consider the stochastic cohen grossberg type bam neural networks with mixed delays by utilizing the lyapunov krasovskii functional and the linear matrix inequality lmi approach some sufficient lmi based conditions are obtained to guarantee the global asymptotic stability of stochastic cohen grossberg type bam neural networks with mixed delays these conditions can be easily checked via the matlab lmi toolbox moreover the obtained results extend and improve the earlier publications finally a numerical example is provided to demonstrate the low conservatism and effectiveness of the proposed lmi conditions

global stability of almost periodic solutions of hopfield neural networks with neutral time varying delays in this paper the global stability and almost periodicity are investigated for hopfield neural networks with neutral time varying delays some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques the results of this paper are new and they complement previously known results

the cev model and its application to financial markets with volatility uncertainty abstract we survey the financial markets whose risks are caused by uncertain volatilities the financial markets focus on the assets which are effectively allocated in one risk free asset and one risky asset whose price process is governed by the constant elasticity of variance c e v for short model which contains the g brownian motion rather than the classical brownian motion such the c e v model which includes the g brownian motion utilized to financial markets is the extension of the classical c e v model applying the concept of arbitrage and the properties of g expectation we consider stock price dynamics which exclude arbitrage opportunities moreover the interval of no arbitrage price for the general european contingent claims is found in the markovian case

delay derivative dependent stability for delayed neural networks with unbound distributed delay in this brief based on lyapunov krasovskii functional approach and appropriate integral inequality a new sufficient condition is derived to guarantee the global stability for delayed neural networks with unbounded distributed delay in which the improved delay partitioning technique and general convex combination are employed the lmi based criterion heavily depends on both the upper and lower bounds on time delay and its derivative which is different from the existent ones and has wider application fields than some present results finally three numerical examples can illustrate the efficiency of the new method based on the reduced conservatism which can be achieved by thinning the delay interval

random recurrent neural networks with delays abstract an infinite lattice model of a recurrent neural network with random connection strengths between neurons is developed and analyzed to incorporate the presence of various type of delays in the neural networks both discrete and distributed time varying delays are considered in the model for the existence of random pullback attractors and periodic attractors the nonlinear terms of the resulting system are not expected to be lipschitz continuous but only satisfy a weaker continuity assumption along with growth conditions under which the uniqueness of the underlying cauchy problem may not hold then after extending the concept and theory of monotone multi valued semiflows to the random context the structure of random pullback attractors with or without periodicity is investigated in particular the existence and stability properties of extremal random complete trajectories are studied

stability and hopf bifurcation of controlled complex networks model with two delays abstract this paper considers hopf bifurcation of complex network with two independent delays by analyzing the eigenvalue equations the local stability of the system is studied taking delay as parameter the change of system stability with time is studied and the emergence of inherent bifurcation is given by changing the value of the delay the bifurcation of a given system can be controlled numerical simulation results confirm the validity of the results found

an analysis of a finite difference and a galerkin technique applied to the simulation of advection and diffusion of air pollutants from a line source abstract a finite difference scheme and a galerkin scheme are compared with respect to a very accurate solution describing time dependent advection and diffusion of air pollutants from a line source in an atmosphere vertically stratified and limited by an inversion layer the accurate solution was achieved by applying the finite difference scheme on a very refined grid with a very small time step the grid size and time step were defined according to stability and accuracy criteria discussed in the text it is found that for the problem considered the two methods can be considered equally accurate however the galerkin method gives a better approximation in the vicinity of the source this was assumed to be partly due to the different way the source term is taken into account in the two methods improvement of the accuracy of the finite difference scheme was achieved by approximating at every step the contribution of the source term by a gaussian puff moving and diffusing with the velocity and diffusivity of the source location instead of utilizing a stepwise function for the numerical approximation of the function representing the source term

pullback attractors for multi valued non compact random dynamical systems generated by reaction diffusion equations on an unbounded domain in this paper we study pullback attractors of reaction diffusion equations on an unbounded domain with non autonomous deterministic as well as stochastic forcing terms for which the uniqueness of solutions need not hold we first present the existence and structure of pullback attractors of multi valued non compact random dynamical systems then we prove the existence of pullback attractors in l2 rn lp rn and h1 rn for multi valued non compact random dynamical systems associated with the reaction diffusion equations on rn and the identical relation of pullback attractors in different spaces is also provided in particular the measurability of pullback attractors is established for reaction diffusion equations on rn

deficient values and angular distribution of entire functions let f z be an entire function of positive and finite order h1 if f z has a finite number of borel directions of order s then the sum of numbers of finite nonzero deficient values of f z and all its primitives does not exceed 21t the proof is based on several lemmas and application of harmonic measure

stability results for stochastic delayed recurrent neural networks with discrete and distributed delays we present new conditions for asymptotic stability and exponential stability of a class of stochastic recurrent neural networks with discrete and distributed time varying delays our approach is based on the method using fixed point theory which do not resort to any liapunov function or liapunov functional our results neither require the boundedness monotonicity and differentiability of the activation functions nor differentiability of the time varying delays in particular a class of neural networks without stochastic perturbations is also considered examples are given to illustrate our main results

dynamic analysis of stochastic cohen grossberg neural networks with time delays abstract in this paper we discuss stochastic cohen grossberg neural networks with time delays by constructing suitable lyapunov functional and employing the semimartingale convergence theorem we give some sufficient criteria ensuring almost sure exponential stability of the networks the results obtained are helpful to design stability of networks when stochastic noise is taken into consideration

stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks in this paper we investigate the stochastic functional differential equations with infinite delay some sufficient conditions are derived to ensure the pth moment exponential stability and pth moment global asymptotic stability of stochastic functional differential equations with infinite delay by using razumikhin method and lyapunov functions based on the obtained results we further study the pth moment exponential stability of stochastic recurrent neural networks with unbounded distributed delays the result extends and improves the earlier publications two examples are given to illustrate the applicability of the obtained results

exponential stability analysis for delayed semi markovian recurrent neural networks a homogeneous polynomial approach this paper investigates the exponential stability analysis issue for a class of delayed recurrent neural networks rnns with semi markovian parameters by constructing a stochastic lyapunov functional and using some zoom techniques to estimate its weak infinitesimal operator the exponential mean square stability criteria have been proposed for the markovian neural networks with certain transition probabilities we then generalize the homogeneous polynomial approach for the delayed markovian rnns with uncertain transition probabilities during the stability analysis theoretical results have obtained by introducing an appropriate technique for dealing with a large number of complex homogeneous polynomial matrix inequalities finally numerical examples are provided to demonstrate the effectiveness of the proposed technique

sufficient and necessary criteria for existence of pullback attractors for non compact random dynamical systems abstract we study pullback attractors of non autonomous non compact dynamical systems generated by differential equations with non autonomous deterministic as well as stochastic forcing terms we first introduce the concepts of pullback attractors and asymptotic compactness for such systems we then prove a sufficient and necessary condition for existence of pullback attractors we also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors for random systems containing periodic deterministic forcing terms we show the pullback attractors are also periodic under certain conditions as an application of the abstract theory we prove the existence of a unique pullback attractor for reaction diffusion equations on r n with both deterministic and random external terms since sobolev embeddings are not compact on unbounded domains the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions

pullback attractors and extremal complete trajectories for non autonomous reaction diffusion problems abstract we analyse the dynamics of the non autonomous nonlinear reaction diffusion equation u t u f t x u subject to appropriate boundary conditions proving the existence of two bounding complete trajectories one maximal and one minimal our main assumption is that the nonlinear term satisfies a bound of the form f t x u u c t x u 2 d t x u where the linear evolution operator associated with c t x is exponentially stable as an important step in our argument we give a detailed analysis of the exponential stability properties of the evolution operator for the non autonomous linear problem u t u c t x u between different l p spaces

on unified concepts of detectability and observability for continuous time stochastic systems this paper is concerned with detectability and observability of continuous time stochastic linear systems by adopting the idea used in defining these two concepts for time varying systems and markovian jump linear systems that have been studied in the literature corresponding definitions for continuous time stochastic linear systems are proposed these two definitions are not only able to unify some recent definitions on these two concept reported in the literature but also allow us to propose an efficient rank criterion to test observability of continuous time stochastic linear systems it seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems with the help of these two concepts and the new criteria the stochastic lyapunov equation is revisited and some recent published work on this equation are generalized numerical examples are given to illustrate the effectiveness of the proposed approach

hybrid stabilization and synchronization of nonlinear systems with unbounded delays the stabilization of nonlinear systems with bounded and unbounded time delays via hybrid control is studied we investigate and identify switching rules for which stabilization can be verified a priori when this approach is inadequate stabilizing state dependent switching rules are constructed this method is based on partitioning the state space into switching regions unwanted physical behavior such as chattering and zeno behavior is avoided sufficient conditions are established using razumikhin like theorems the theoretical results provide insight into how hybrid control strategies can be constructed to synchronize a class of nonlinear systems with unbounded delay the findings are illustrated through numerical simulations

exponential mean square stability of time delay singular systems with markovian switching and nonlinear perturbations abstract this paper considers exponential stability in mean square of singular markovian jump systems the systems under consideration involve nonlinear perturbation and time varying delays by using the lyapunov krasovskii functional delay dependent stability conditions in terms of linear matrix inequality lmi are addressed which guarantee exponential mean square stability and a prescribed h performance index for the considered systems two numerical examples are given to illustrate the effectiveness of the proposed main results

dynamical behaviors of a large class of general delayed neural networks research of delayed neural networks with varying self inhibitions interconnection weights and inputs is an important issue in the real world self inhibitions interconnection weights and inputs should vary as time varies in this letter we discuss a large class of delayed neural networks with periodic inhibitions interconnection weights and inputs we prove that if the activation functions are of lipschitz type and some set of inequalities for example the set of inequalities 3 1 in theorem 1 is satisfied the delayed system has a unique periodic solution and any solution will converge to this periodic solution we also prove that if either set of inequalities 3 20 in theorem 2 or 3 23 in theorem 3 is satisfied then the system is exponentially stable globally this class of delayed dynamical systems provides a general framework for many delayed dynamical systems as special cases it includes delayed hopfield neural networks and cellular neural networks as well as distributed delayed neural networks with periodic self inhibitions interconnection weights and inputs moreover the entire discussion applies to delayed systems with constant self inhibitions interconnection weights and inputs

global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances this paper is concerned with the synchronization problem for a new class of continuous time delayed complex networks with stochastic nonlinearities randomly occurring nonlinearities interval time varying delays unbounded distributed delays as well as multiple stochastic disturbances the stochastic nonlinearities and multiple stochastic disturbances are investigated here in order to reflect more realistic dynamical behaviors of the complex networks that are affected by the noisy environment by utilizing a new matrix functional with the idea of partitioning the lower bound 1 of the time varying delay we employ the stochastic analysis techniques and the properties of the kronecker product to establish delay dependent synchronization criteria that ensure the globally asymptotically mean square synchronization of the addressed stochastic delayed complex networks the sufficient conditions obtained are in the form of linear matrix inequalities lmis whose solutions can be readily solved by using the standard numerical software a numerical example is exploited to show the applicability of the proposed results

global asymptotic stability of stochastic recurrent neural networks with multiple discrete delays and unbounded distributed delays abstract in this paper using lyapunov krasovskii functional and the linear matrix inequality lmi approach the global asymptotic stability of stochastic recurrent neural networks with multiple discrete time varying delays and distributed delays is analyzed a new sufficient condition ensuring the global asymptotic stability for delayed recurrent neural networks is obtained in the stochastic sense using the powerful matlab lmi toolbox two examples are provided to illustrate the applicability of the stability results

an analysis of global asymptotic stability of delayed cellular neural networks in this paper a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks dcnns this condition imposes constraints on the feedback and delayed feedback matrices of a dcnn independently of the delay parameter this result is also compared with the previous results derived in the literature

projective synchronization of different chaotic time delayed neural networks based on integral sliding mode controller in this paper an integral sliding mode control approach is presented to study the projective synchronization for different chaotic time delayed neural networks a sliding mode surface is appropriately constructed and a sliding mode controller is synthesized to guarantee the reachability of the specified sliding surface the global asymptotic stability of the error dynamical system in the specified switching surface is investigated with the lyapunov krasovskii l k functional method a delay dependent sufficient condition is derived and the maximum time delay value is obtained by means of the linear matrix inequality lmi technique a simulation example is finally exploited to illustrate the feasibility and effectiveness of the proposed approach verify the conservativeness of l k method and lmi technique and exhibit the relationship between the convergence velocity of error system and the gain matrix