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Items from 1 to 20 out of 105 results

article

Dynamical analysis of a stage structured predator–prey system with impulsive diffusion and generic functional response

Yuanfu Shao, Ying Li, Y. Shao, Y. Li

Applied Mathematics and Computation > 2013 > 220 > Complete > 472-481

Based on the predator–prey system with stage structure and generalized functional response, an impulsive differential system to model the process of periodical diffusion at different fixed time is proposed and investigated. By using comparison theorem of impulsive differential equation and some analysis techniques, sufficient conditions ensuring the existence of a predator-extinction positive periodic...

article

The attractivity of functional hereditary integral equations

Qingxiang Fang, Xiaoping Liu, Jigen Peng

Mathematical Methods in the Applied Sciences > 46 > 2 > 1821 - 1836

In this paper, the problem of attractivity of solutions for functional hereditary integral equations is initiated. A hereditary integral equation is converted into a second kind Volterra integral equation of convolution type by use of the property of convolution. Sufficient conditions for the existence of attractive solutions are established according to the fixed point theorem. The conclusions presented...

article

Where science, technology, engineering, and mathematics (STEM) graduates move: Human capital, employment patterns, and interstate migration in the United States

Richard Wright, Mark Ellis

Population, Space and Place > 25 > 4 > n/a - n/a

This research investigates the interstate migration of workers in the United States who have earned an undergraduate STEM (science, technology, engineering, and mathematics) degree compared with those who have not. We build on previous studies that (a) classified “skilled” workers as having earned an undergraduate degree (b) used net migration gain or loss as a yardstick of relative destination attraction,...

article

On a Multi-Delay Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion

Changyou Wang, Nan Li, Yuqian Zhou, Xingcheng Pu, more

Acta Mathematica Scientia > 2019 > 39 > 2 > 429-448

This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the globally attractivity of positive...

article

Global dynamic scenarios for competitive maps in the plane

Elliott Bertrand, M. R. S. Kulenović

Advances in Difference Equations > 2018 > 2018 > 1 > 1-28

In this paper we present some global dynamic scenarios for general competitive maps in the plane. We apply these results to the class of second-order autonomous difference equations whose transition functions are decreasing in the variable xn $x_{n}$ and increasing in the variable xn−1 $x_{n-1}$. We illustrate our results with the application to the difference equation xn+1=Cxn−12+Exn−1axn2+dxn+f,n=0,1,…,...

article

Well-posedness of a ratio-dependent Lotka–Volterra system with feedback control

Changyou Wang, Yuqian Zhou, Yonghong Li, Rui Li

Boundary Value Problems > 2018 > 2018 > 1 > 1-16

The main purpose of this article is to consider a Lotka–Volterra predator–prey system with ratio-dependent functional responses and feedback controls. By using a comparison theorem and constructing a suitable Lyapunov function as well as developing some new analysis techniques, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the global...

article

Existence and attractivity of solutions for fractional difference equations

Lu Zhang, Yong Zhou

Advances in Difference Equations > 2018 > 2018 > 1 > 1-15

In this paper, we study a kind of difference equations with Riemann–Liouville-like fractional difference. The results on existence and attractivity are obtained by using the Picard iteration method and Schauder’s fixed point theorem. Examples are provided to illustrate the main results.

article

Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces

S. Abbas, R. P. Agarwal, M. Benchohra, F. Berhoun

Demonstratio Mathematica > 2018 > Vol. 51, nr 1 > 131--140

In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Hadamard fractional order. We use an extension of the Burton-Kirk fixed point theorem in Fréchet spaces.

article

A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

Saïd Abbas, Mouffak Benchohra, Jamal-Eddine Lazreg, Yong Zhou

Chaos, Solitons & Fractals > 2017 > 102 > C > 47-71

In the present survey paper, we prove some results concerning the existence of solutions and weak solutions for some classes of Hadamard and Hilfer fractional differential equations. Some attractivity and Ulam stability results are presented. Our results are provided by applying the fixed point theory, and the technique of strong and weak measures of noncompactness.

article

Global attractivity of memristor-based fractional-order neural networks

Shuo Zhang, Yongguang Yu, Yajuan Gu

Neurocomputing > 2017 > 227 > C > 64-73

Some dynamical properties, especially the global attractivity, of memristor-based fractional-order neural networks (FNN) are discussed. By using Filippov solutions, the existence of memristor-based FNN's solutions is firstly guaranteed under a growth condition. With non-Lipschitz neuron activations, different dynamics of memristor-based FNN are analyzed by employing the Lyapunov functionals. Then,...

article

Single-species model under seasonal succession alternating between Gompertz and Logistic growth and impulsive perturbations

Yanqing Li, Long Zhang, Zhidong Teng

GEM - International Journal on Geomathematics > 2017 > 8 > 2 > 241-260

This paper proposes a single species system under seasonal succession and impulsive perturbations. The system is composed of two processes: one governed by the Gompertz equation, and the other modelled by the Logistic equation. The two processes are connected by impulse perturbations. Some very general, weak criteria on the permanence, existence, uniqueness and global stability of the positive periodic...

article

Modulation equation for SPDEs in unbounded domains with space–time white noise — Linear theory

Luigi Amedeo Bianchi, Dirk Blömker

Stochastic Processes and their Applications > 2016 > 126 > 10 > 3171-3201

We study the approximation of SPDEs on the whole real line near a change of stability via modulation or amplitude equations, which acts as a replacement for the lack of random invariant manifolds on extended domains. Due to the unboundedness of the underlying domain a whole band of infinitely many eigenfunctions changes stability. Thus we expect not only a slow motion in time, but also a slow spatial...

article

Multiperiodicity and Exponential Attractivity of Neural Networks with Mixed Delays

Yan Ji, Feng Ding

Circuits, Systems, and Signal Processing > 2017 > 36 > 6 > 2558-2573

This paper studies the multiperiodicity and exponential attractivity evoked by periodic external inputs in cellular neural networks with discrete delays and distributed delays. We show that an n-neuron cellular neural network with mixed delays can have $$2^n$$ 2 n periodic orbits located in saturation regions and these periodic orbits are locally exponentially attractive. Besides, some...

article

Attractivity of the recursive sequence xn+1=(A−Bxn−2)/(C+Dxn−1)

A.M. Ahmed, N.A. Eshtewy

Journal of the Egyptian Mathematical Society > 2016 > 24 > 3 > 392-395

In this paper, we investigate the global attractivity of the difference equationxn+1=A−Bxn−2C+Dxn−1,n=0,1,…,where A, B are nonnegative real numbers, C, D are positive real numbers and C+Dxn−1≠0 for all n ≥ 0.

article

Global dynamics and bifurcation of a perturbed Sigmoid Beverton–Holt difference equation

M. R. S. Kulenović, S. Moranjkić, Z. Nurkanović

Mathematical Methods in the Applied Sciences > 39 > 10 > 2696 - 2715

T. Wanner We investigate global dynamics of the equation where the parameters b,c, and f are nonnegative numbers with condition b + c > 0,f ≠ 0 and the initial conditions x₋₁,x₀ are arbitrary nonnegative numbers such that x₋₁+x₀>0. We obtain precise characterization of basins of attraction of all attractors of this equation and describe the dynamics in terms of bifurcations of period‐two solutions...

article

Global existence and stability for functional evolution equations with state-dependent delay

Eman Alaidarous, Wafaa Albarakati, Abdessalam Baliki, Mouffak Benchohra

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales.... > 2017 > 111 > 1 > 15-24

In this paper we prove some results on the global existence and attractivity of mild solutions for semilinear evolution equations with state-dependent delay in Banach space.

article

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Saïd Abbas, Mouffak Benchohra, Johnny Henderson, Boualem Attou Slimani

Journal of Applied Mathematics and Computing > 2016 > 52 > 1-2 > 73-85

In this paper, we prove an existence result and we initiate the question of attractivity of solutions for initial value problems (IVP for short), for fractional order neutral differential equations with finite delay. The proof of the main result is based on Krasnosel’skii’s fixed point theorem.

article

Global Dynamics and Bifurcations of Certain Second Order Rational Difference Equation with Quadratic Terms

Sabina Jašarević Hrustić, M. R. S. Kulenović, M. Nurkanović

Qualitative Theory of Dynamical Systems > 2016 > 15 > 1 > 283-307

We investigate global dynamics of the equation $$\begin{aligned} x_{n+1}=\frac{x_{n-1}}{ax_{n}^{2}+ex_{n-1}+f},\quad n=0,1,2,\ldots , \end{aligned}$$ x n + 1 = x n - 1 a x n 2 + e x n - 1 + f , n = 0 , 1 , 2 , … , where the parameters a, e and f are nonnegative numbers with condition $$a+e+f>0$$ a + e + f > 0 and the initial conditions $$x_{-1},x_{0}$$...

article

Basins of attraction of period-two solutions of monotone difference equations

Arzu Bilgin, Mustafa Rs Kulenović, Esmir Pilav

Advances in Difference Equations > 2016 > 2016 > 1 > 1-25

We investigate the global character of the difference equation of the form x n + 1 = f ( x n , x n − 1 ) , n = 0 , 1 , … $$x_{n+1} = f(x_{n}, x_{n-1}),\quad n=0,1, \ldots $$ with several period-two solutions, where f is increasing in all its variables. We show that the boundaries of the basins of attractions of different locally asymptotically stable equilibrium solutions or period-two...

article

Existence and attractivity of global solutions for a class of fractional quadratic integral equations in Banach space

Huiwen Wang, Fang Li

Advances in Difference Equations > 2016 > 2016 > 1 > 1-15

In this paper, we present some results concerning the existence and attractivity of global solutions for a class of nonlinear fractional integral equations and fractional differential equations in a Banach space X, respectively. These results are new even in the case of X = R $X=\mathbf{R}$ . Some examples are given to show the applications of the abstract results.

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Dynamical analysis of a stage structured predator–prey system with impulsive diffusion and generic functional response

The attractivity of functional hereditary integral equations

Where science, technology, engineering, and mathematics (STEM) graduates move: Human capital, employment patterns, and interstate migration in the United States

On a Multi-Delay Lotka-Volterra Predator-Prey Model with Feedback Controls and Prey Diffusion

Global dynamic scenarios for competitive maps in the plane

Well-posedness of a ratio-dependent Lotka–Volterra system with feedback control

Existence and attractivity of solutions for fractional difference equations

Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces

A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability

Global attractivity of memristor-based fractional-order neural networks

Single-species model under seasonal succession alternating between Gompertz and Logistic growth and impulsive perturbations

Modulation equation for SPDEs in unbounded domains with space–time white noise — Linear theory

Multiperiodicity and Exponential Attractivity of Neural Networks with Mixed Delays

Attractivity of the recursive sequence xn+1=(A−Bxn−2)/(C+Dxn−1)

Global dynamics and bifurcation of a perturbed Sigmoid Beverton–Holt difference equation

Global existence and stability for functional evolution equations with state-dependent delay

Existence and attractivity for the Darboux problem of fractional order neutral differential equations

Global Dynamics and Bifurcations of Certain Second Order Rational Difference Equation with Quadratic Terms

Basins of attraction of period-two solutions of monotone difference equations

Existence and attractivity of global solutions for a class of fractional quadratic integral equations in Banach space

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