Showing papers in "Journal of Applied Analysis and Computation in 2016"
TL;DR: In this paper, the authors developed a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment, which can also be used to explore the threshold for the deterministic deterministic Chemostat models.
Abstract: This paper intends to develop a new method to obtain the threshold of an impulsive stochastic chemostat model with saturated growth rate in a polluted environment. By using the theory of impulsive differential equations and stochastic differential equations, we obtain conditions for the extinction and the permanence of the microorganisms of the deterministic chemostat model and the stochastic chemostat model. We develop a new numerical computation method for impulsive stochastic differential system to simulate and illustrate our theoretical conclusions. The biological results show that a small stochastic disturbance can cause the microorganism to die out, that is, a permanent deterministic system can go to extinction under the white noise stochastic disturbance. The theoretical method can also be used to explore the threshold of some impulsive stochastic differential equations.
90 citations
TL;DR: In this paper, a new SIV epidemic model with time delay, which also involves both direct and environmental transmissions, was proposed, and global stability of the equilibria was discussed by means of Lyapunov functionals and LaSalle invariance principle for delay differential equations, which showed that the infection-free equilibrium of the system is globally asymptotically stable if R 1:
Abstract: In this paper, we propose a new SIV epidemic model with time delay, which also involves both direct and environmental transmissions. For such model, we first introduce the basic reproduction number R by using the next generation matrix. And then global stability of the equilibria is discussed by means of Lyapunov functionals and LaSalle's invariance principle for delay differential equations, which shows that the infection-free equilibrium of the system is globally asymptotically stable if R 1:
54 citations
TL;DR: This paper calculates the number of spanning trees in prism and antiprism graphs corresponding to the skeleton of a prism and an antiprisms by the electrically equivalent transformations and rules of weighted generating function and derives the analytical expressions for enumeration of spanning Trees.
Abstract: In this paper, we calculate the number of spanning trees in prism and antiprism graphs corresponding to the skeleton of a prism and an antiprism. By the electrically equivalent transformations and rules of weighted generating function, we obtain a relationship for the weighted number of spanning trees at the successive two generations. Using the knowledge of difference equations, we derive the analytical expressions for enumeration of spanning trees. In addition, we again calculate the number of spanning trees in Apollonian networks, which shows that this method is simple and effective. Finally we compare the entropy of our networks with other studied networks and find that the entropy of the antiprism graph is larger.
37 citations
TL;DR: In this article, a new divergence measure for intuitionistic fuzzy sets (IFS) and its interesting properties are studied and a parameter α is incorporated in the proposed divergence measure and it is defined as parametric intuitionistic fuzz divergence measure (PIFDM).
Abstract: As far as medical diagnosis problem is concerned, predicting the actual disease in complex situations has been a concerning matter for the doctors/experts. The divergence measure for intuitionistic fuzzy sets is an effective and potent tool in addressing the medical decision making problems. We define a new divergence measure for intuitionistic fuzzy sets (IFS) and its interesting properties are studied. The existing divergence measures under intuitionistic fuzzy environment are reviewed and their counter-intuitive cases has been explored. The parameter α is incorporated in the proposed divergence measure and it is defined as parametric intuitionistic fuzzy divergence measure (PIFDM). The different choices of the parameter α provide different decisions about the disease. As we increase the value of α, the information about the disease increases and move towards the optimal solution with the reduced in the uncertainty. Finally, we compare our results with the already existing results, which illustrate the role of the parameter α in obtaining the optimal solution in the medical decision making application. The results demonstrate that the parametric intuitionistic fuzzy divergence measure (PIFDM) is more comprehensive and effective than the proposed intuitionistic fuzzy divergence measure and the existing intuitionistic fuzzy divergence measures for decision making in medical investigations.
28 citations
TL;DR: To find the optimal transportation units a time and space based with order of convergence O(MN) meta-heuristic Genetic Algorithm have been proposed and the equivalent crisp model so obtained are solved by using LINGO 13.0.
Abstract: In this paper, we have introduced a Solid Transportation Problem where the constrains are mixed type. The model is developed under different environment like, crisp, fuzzy and intuitionistic fuzzy etc. Using the interval approximation method we defuzzify the fuzzy amount and for intuitionistic fuzzy set we use the (α,β)-cut sets to get the corresponding crisp amount. To find the optimal transportation units a time and space based with order of convergence O(MN2) meta-heuristic Genetic Algorithm have been proposed. Also the equivalent crisp model so obtained are solved by using LINGO 13.0. The results obtained using GA treats as the best solution by comparing with LINGO results for this present study. The proposed models and techniques are finally illustrated by providing numerical examples. Degree of efficiency have been find out for both the algorithm.
23 citations
TL;DR: In this paper, the global stability of the endemic equilibrium of the SIR epidemic model with nonlinear incidence was proved by introducing a variable transformation and constructing a more general Lyapunov function.
Abstract: In this paper, by investigating an SIR epidemic model with nonlinear incidence, we present a new technique for proving the global stability of the endemic equilibrium, which consists of introducing a variable transformation and constructing a more general Lyapunov function. For the model we obtain the following results. The disease-free equilibrium is globally stable in the feasible region as the basic reproduction number is less than or equal to unity, and the endemic equilibrium is globally stable in the feasible region as the basic reproduction number is greater than unity. The generality of the technique is illustrated by considering certain nonlinear incidences and SIS and SIRS epidemic models.
22 citations
TL;DR: In this article, He's Variational Iteration method (VIM) was used for solving nonlinear Newell-Whitehead-Segel equation and three different cases of NWS equation have been discussed.
Abstract: In this paper, we apply He's Variational iteration method (VIM) for solving nonlinear Newell-Whitehead-Segel equation. By using this method three different cases of Newell-Whitehead-Segel equation have been discussed. Comparison of the obtained result with exact solutions shows that the method used is an effective and highly promising method for solving different cases of nonlinear Newell-Whitehead-Segel equation.
21 citations
TL;DR: Using the method of dynamical systems for the generalized Radhakrishnan, Kundu, Lakshmanan equation, the existence of soliton solutions, uncountably infinite many periodic wave solutions and unbounded wave solution are obtained as mentioned in this paper.
Abstract: Using the method of dynamical systems for the the generalized Radhakrishnan, Kundu, Lakshmanan equation, the existence of soliton solutions, uncountably infinite many periodic wave solutions and unbounded wave solution are obtained. Exact explicit parametric representations of the above travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.
18 citations
TL;DR: By bridging a generalized memristor between a passive LC oscillator and an active RC filter, a simple and feasible memristive Chua's circuit is presented in this paper, which is equivalently achieved by a full-wave rectifier cascaded with a first-order parallel RC filter.
Abstract: By bridging a generalized memristor between a passive LC oscillator and an active RC filter, a simple and feasible memristive Chua's circuit is presented. The generalized memristor without grounded limitation is equivalently achieved by a full-wave rectifier cascaded with a first-order parallel RC filter. The dynamical characteristics of the proposed circuit are investigated both theoretically and numerically, from which it can be found that the circuit has three unstable equilibrium points and demonstrates complex nonlinear phenomena. The experimental circuit is easy to implement and the measurement results validate the results of theoretical analyses.
16 citations
TL;DR: A general approach is proposed to generate n-dimensional multi-scroll Jerk chaotic attractors via nonlinear control and it is shown that the method of obtaining complex Jerk chaos attractors is effective.
Abstract: Based on three-order Jerk and high-order Jerk chaotic systems, a general approach is proposed to generate n-dimensional multi-scroll Jerk chaotic attractors via nonlinear control. Dynamics of the n-dimensional multiscroll Jerk chaotic systems are analyzed by means of the largest Lyapunov exponent and multi-scale permutation entropy complexity. As an experimental verification, four-dimensional Jerk chaotic attractors are implemented by analog circuits. Results of the numerical simulation are consistent with that of the hardware experiments. It shows that the method of obtaining complex Jerk chaotic attractors is effective.
13 citations
TL;DR: In this article, it was shown that convolutions of planar harmonic mappings which are convex in the direction of the real axis are also convex along the same direction.
Abstract: In this paper, we show that convolutions of some planar harmonic mappings which convex in the direction of the real axis are also convex in the same direction. Furthermore, by means of the Mathematica software, we present an example to illuminate the main result.
TL;DR: In this paper, the existence and multiplicity of positive solutions for a system of higher-order nonlinear fractional differential equations with nonlocal boundary conditions was proved using fixed point index theory in cone.
Abstract: The paper deals with the existence and multiplicity of positive solutions for a system of higher-order nonlinear fractional differential equations with nonlocal boundary conditions. The main tool used in the proof is fixed point index theory in cone. Some limit type conditions for ensuring the existence of positive solutions are given.
TL;DR: In this paper, the stability of 2D magnetohydrodynamics (MHD) equations perturbed by multiplicative noises in both the velocity and the magnetic field is studied.
Abstract: In this paper, 2-dimensional (2D) magnetohydrodynamics (MHD) equations perturbed by multiplicative noises in both the velocity and the magnetic field is studied. We first considered the stability, or the upper semicontinuity, for equivalent random dynamical systems (RDS), and then applying the abstract result we established the existence and the upper semi-continuity of tempered random attractors for the stochastic MHD equations. This result shows that the asymptotic behavior of MHD equations is stable under stochastic perturbations.
TL;DR: In this article, it was shown that every (Q, T)-affine-periodic differential equation has a solution with exponential dichotomy or exponential trichotomy if the corresponding homogeneous linear equation admits an identity matrix or orthogonal matrix.
Abstract: It is proved that every (Q, T)-affine-periodic differential equation has a (Q, T)-affine-periodic solution if the corresponding homogeneous linear equation admits exponential dichotomy or exponential trichotomy. This kind of "periodic" solutions might be usual periodic or quasi-periodic ones if Q is an identity matrix or orthogonal matrix. Hence solutions also possess certain symmetry in geometry. The result is also extended to the case of pseudo affine-periodic solutions.
TL;DR: In this article, a heroin epidemic model on complex networks is proposed and the basic reproduction number R 0 is obtained by the next generation matrix, and if R 0 1, there is an unique endemic equilibrium and it is also globally asymptotically stable.
Abstract: In this paper, a heroin epidemic model on complex networks is proposed. By the next generation matrix, the basic reproduction number R0 is obtained. If R0 1, there is an unique endemic equilibrium and it is also globally asymptotically stable. Our results show that if the degree of the network is large enough, the drug transmission always spreads. Sensitivity analysis of the basic reproduction number with the various parameters in the model are carried out to verify the important effects for control the drug transmission. Some simulations illustrate our theoretical results.
TL;DR: In this paper, the fuzzy Basset equation is introduced and the authors investigated the existence and uniqueness of solution with converting the problem to a system of fuzzy fractional differential equation, and the solution is also obtained under Caputo generalized Hukuhara differentiability.
Abstract: In this paper, the fuzzy Basset equation is introduced. This problem is related to the motion of a sphere in a viscous liquid when its parameters are fuzzy numbers. We investigate the existence and uniqueness of solution with converting the problem to a system of fuzzy fractional differential equation, and the solution is also obtained under Caputo generalized Hukuhara differentiability. Some examples show the effectiveness and efficiency our approach.
TL;DR: In this article, an appropriate inventory model for non-instantaneous deteriorating items over quadratic demand rate with permissible delay in payments and time dependent deterioration rate was proposed, where completely backlogged shortages are allowed.
Abstract: In this paper, we propose an appropriate inventory model for noninstantaneous deteriorating items over quadratic demand rate with permissible delay in payments and time dependent deterioration rate. In this model, the completely backlogged shortages are allowed. In several existing results, the authors discussed that the deterioration rate is constant in each cycle. However, the deterioration rate of items are not constant in real world applications. Motivated by this fact, we consider that the items are deteriorated with respect to time. To minimize the total relevant inventory cost, we prove some useful theorems to illustrate the optimal solutions by finding an optimal cycle time with the necessary and enough conditions for the existence and uniqueness of the optimal solutions. Finally, we discuss the numerical instance and sensitivity of the proposed model.
TL;DR: In this paper, the generalized Rankine-Hugoniot conditions and entropy con- dition were used to obtain the global existence of generalized solutions including delta shock waves that explicitly exhibit four kinds of dierent struc- tures.
Abstract: In this paper, we study the Riemann problem with the initial data containing the Dirac delta function for the relativistic Chaplygin Euler equa- tions. Under the generalized Rankine-Hugoniot conditions and entropy con- dition, we constructively obtain the global existence of generalized solutions including delta shock waves that explicitly exhibit four kinds of dierent struc- tures. Moreover, we obtain the stability of generalized solutions by making use of the perturbation of the initial data.
TL;DR: In this paper, the error analysis of three time-stepping schemes used in the discretization of a nonlinear reaction-diffusion equation with Neumann boundary conditions, relevant in phase transition, is presented.
Abstract: Abstract We present the error analysis of three time-stepping schemes used in the discretization of a nonlinear reaction-diffusion equation with Neumann boundary conditions, relevant in phase transition. We prove L∞ stability by maximum principle arguments, and derive error estimates using energy methods for the implicit Euler, and two implicit-explicit approaches, a linearized scheme and a fractional step method. A numerical experiment validates the theoretical results, comparing the accuracy of the methods.
TL;DR: In this article, the authors proved that the solution of the backward Euler scheme applied to a damped wave equation with analytic nonlinearity converges to a stationary solution as time goes to infinity.
Abstract: We prove that the solution of the backward Euler scheme applied to a damped wave equation with analytic nonlinearity converges to a stationary solution as time goes to infinity. The proof is based on the Łojasiewciz-Simon inequality. It is much simpler than in the continuous case, thanks to the dissipativity of the scheme. The framework includes the modified Allen-Cahn equation and the sine-Gordon equation.
TL;DR: The main features, several typical examples and the main progress for NON are outlined, including the epidemic spreading in multilayer coupled networks.
Abstract: In the era of big data, network science is facing new challenges and opportunities. This review article focuses on discussing one of the hottest subjects of network science “network of networks” (NON). The main features, several typical examples and the main progress for NON are outlined, including the epidemic spreading in multilayer coupled networks. Finally the most challenging tasks for NON are proposed.
TL;DR: In this article, a class of Mittag-Leffler type multivariable functions is studied and convergence conditions for these functions are established, and several properties associated with this class and those related with the corresponding class of fractional integral operators are discussed.
Abstract: The present paper studies and investigates a class of Mittag-Leffler type multivariable functions. We derive the necessary convergence conditions and establish several properties associated with this class and those related with the corresponding class of fractional integral operators. New extensions of the introduced definitions and special cases of some of the results are also pointed out.
TL;DR: In this article, an improved DBC-based approach was proposed to optimize the performance of the method in the following ways: reducing fitting errors by decreasing step lengths, considering under-counting boxes on the border of two neighboring box-blocks and making better use of all the pixels in the blocks while not neglecting the middle parts.
Abstract: Fractal dimension (FD) reflects the intrinsic self-similarity of an image and can be used in image classification, image segmentation and texture analysis. The differential box-counting (DBC) method is a common approach to calculating the FD values. This paper proposes an improved DBC-based approach to optimizing the performance of the method in the following ways:reducing fitting errors by decreasing step lengths, considering under-counting boxes on the border of two neighboring box-blocks and making better use of all the pixels in the blocks while not neglecting the middle parts. The experimental results show that the fitting error of the new method can be decreased to 0.012879. The average distance of the FD values is decreased by 16.0% in the divided images and the average variance of the FD values is decreased by 30% in the scaled images, compared with other modified methods. The results show that the new method has a better performance in the recognition of the same type of images and the scaled images.
TL;DR: In this paper, the authors investigated a class of multi-group epidemic models with general exposed distribution and nonlinear incidence rate, and they showed that the global dynamics are completely determined by the basic production number R0.
Abstract: In this paper, we investigate a class of multi-group epidemic models with general exposed distribution and nonlinear incidence rate. Under biologi- cally motivated assumptions, we show that the global dynamics are completely determined by the basic production number R0. The disease-free equilibrium is globally asymptotically stable if R0 1, and there exists a unique endem- ic equilibrium which is globally asymptotically stable if R0 > 1. The proofs of the main results exploit the persistence theory in dynamical system and a graph-theoretical approach to the method of Lyapunov functionals. A simpler case that assumes an identical natural death rate for all groups and a gam- ma distribution for exposed distribution is also considered. In addition, two numerical examples are showed to illustrate the results.
TL;DR: In this paper, the authors studied the approximate controllability of second order impulsive functional differential systems with infinite delay in Banach spaces, and proved sufficient conditions for the approximation of the controllable part of the system under the assumption that the associated linear part of system is approximately controLLable.
Abstract: This paper studies the approximate controllability of second order impulsive functional differential system with infinite delay in Banach spaces. Sufficient conditions are formulated and proved for the approximate controllability of such system under the assumption that the associated linear part of system is approximately controllable. The results are obtained by using strongly continuous cosine families of operators and the contraction mapping principle. An example is given to illustrate the obtained theory.
TL;DR: In this article, a fixed point index theory was developed for a class of compact maps defined on a cone which do not necessarily take values in the cone, and applied to treat some abstract boundary value problems.
Abstract: A fixed point index theory is developed for a class of nowhere normal-outward compact maps defined on a cone which do not necessarily take values in the cone. This class depends on the retractions on the cone and contains self-maps for any retractions, and weakly inward maps and generalized inward maps when the retraction is a continuous metric projection. The new index coincides with the previous fixed point index theories for compact self-maps and generalized inward compact maps. New fixed point theorems are obtained for nowhere normal-outward compact maps and applied to treat some abstract boundary value problems and Sturm-Liouville boundary value problems with nonlinearities changing signs.
TL;DR: In this paper, a class of second order difference equations with three paremeters is studied and the asymptotic behavior of positive solutions with positive initial values is investigated.
Abstract: In this paper, we study a class of second order difference equations with three paremeters. With positive initial values, the asymptotic behavior of positive solutions are investigated.
TL;DR: In this article, the Hermite-Hadamard integral inequalities for (α, m)-preinvex mappings are established for n-times differentiable mappings.
Abstract: We establish various inequalities for n-times differentiable mappings that are connected with illustrious Hermite-Hadamard integral inequality for mapping whose absolute values of derivatives are (α, m)-preinvex function. The new integral inequalities are then applied to some special means.
TL;DR: In this paper, the authors introduced the notion of (α, m, P)-convex functions on co-ordinates and established new integral inequalities of Hermite-Hadamard type for these functions.
Abstract: In the paper, the authors introduce the notion "(α, m; P)-convex function on co-ordinates" and establish new integral inequalities of Hermite-Hadamard type for (α, m; P)-convex functions on co-ordinates in a rectangle from the plane R0×R.