Paper's Title:

Existence and Approximation of Traveling Wavefronts for the Diffusive Mackey-Glass Equation

Author(s):

C. Ramirez-Carrasco and J. Molina-Garay

Facultad de Ciencias Basicas,
Universidad Catolica del Maule, Talca,
Chile
E-mail: carloshrc1989@gmail.com
 molina@imca.edu.pe

Abstract:

In this paper, we consider the diffusive Mackey-Glass model with discrete delay. This equation describes the dynamics of the blood cell production. We investigate the existence of traveling wavefronts solutions connecting the two steady states of the model. We develop an alternative proof of the existence of such solutions and we also demonstrate the existence of traveling wavefronts moving at minimum speed. The proposed approach is based on the use technique of upper-lower solutions. Finally, through an iterative procedure, we show numerical simulations that approximate the traveling wavefronts, thus confirming our theoretical results.

Paper's Title:

Topological Aspects of Discrete Switch Dynamical Systems

Author(s):

Faiz Imam and Sharan Gopal

Department of Mathematics,
BITS - Pilani, Hyderabad Campus,
India.
E-mail: mefaizy@gmail.com

Department of Mathematics,
BITS - Pilani, Hyderabad Campus,
India.
E-mail: sharanraghu@gmail.com

ABSTRACT NOT FOUND. WEBSITE ERROR

Abstract:

Paper's Title:

On Infinite Unions and Intersections of Sets in a Metric Space

Author(s):

Spiros Konstantogiannis

Ronin Institute,
Montclair, New Jersey,
United States.
E-mail: spiros.konstantogiannis@ronininstitute.org
URL: https://www.researchgate.net/profile/Spiros-Konstantogiannis

Abstract:

The aim of this paper is to examine infinite unions and intersections of sets in a general metric space, with a view to explaining when an infinite intersection of open sets is an open set and when an infinite union of closed sets is a closed set.

Paper's Title:

The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations

Author(s):

Alexandru Mihai Bica

Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro

Abstract:

We present here a numerical method for first order delay ordinary differential equations, which use the Banach's fixed point theorem, the sequence of successive approximations and the trapezoidal quadrature rule. The error estimation of the method uses a recent result of P. Cerone and S.S. Dragomir about the remainder of the trapezoidal quadrature rule for Lipchitzian functions and for functions with continuous first derivative.

Paper's Title:

A new approach to the study of fixed point for simulation functions with application in G-metric spaces

Author(s):

Komi Afassinou and Ojen Kumar Narain

Department of Mathematical Sciences, University of Zululand,
KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

The purpose of this work is to generalize the fixed point results of Kumar et al. [11] by introducing the concept of (α,β)-Z-contraction mapping, Suzuki generalized (α,β)-Z-contraction mapping, (α,β)-admissible mapping and triangular (α,β)-admissible mapping in the frame work of G-metric spaces. Fixed point theorems for these class of mappings are established in the frame work of a complete G-metric spaces and we establish a generalization of the fixed point result of Kumar et al. [11] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.

Paper's Title:

Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators

Author(s):

B. Deruni¹, A. S. Hacinliyan^1,2, E. Kandiran³, A. C. Keles², S. Kaouache⁴, M.-S. Abdelouahab⁴, N.-E. Hamri⁴

¹Department of Physics,
University of Yeditepe,
Turkey.

²Department of Information Systems and Technologies,
University of Yeditepe,
Turkey

³Department of Software Development,
University of Yeditepe,
Turkey.

⁴Laboratory of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.

E-mail: berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centr-univ-mila.dz
medsalah3@yahoo.fr
n.hamri@centre-univ-mila.dz

Abstract:

In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.

Paper's Title:

Optimal Conditions using Multi-valued G-Presic type Mapping

Author(s):

Deb Sarkar, Ramakant Bhardwaj, Vandana Rathore, and Pulak Konar

Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: debsarkar1996@gmail.com

Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: drrkbhardwaj100@gmail.com

School of Engineering and Technology,
Jagran Lakecity University, Bhopal, MP-462044,
India.
E-mail: drvandana@jlu.edu.in

Department of Mathematics,
VIT University, Chennai, Tamil Nadu-600127,
India.
E-mail: pulakkonar@gmail.com

Abstract:

In the present paper, some best proximity results have been presented using the concept of G-Presic type multi-valued mapping. These results are the extensions of Presic's theorem in the non-self mapping. A suitable example has also been given. Here, some applications are presented in θ-chainable space and ordered metric space.

Paper's Title:

Oscillation Criteria for Second Order Delay Difference Equations via Canonical Transformations and Some New Monotonic Properties

Author(s):

R. Deepalakhmi, S. Saravanan, J. R. Graef, and E. Thandapani

Department of Interdisciplinary Studies
Tamil Nadu Dr. Ambedkar Law University
Chennai-600113,
India.
profdeepalakshmi@gmail.com

Madras School of Economics,
Chennai-600025,
India.
profsaran11@gmail.com

Department of Mathematics,
University of Tennessee at Chattanooga,
Chattanooga,TN 37403,
USA.
john-graef@utc.edu

Ramanujan Institute for Advanced Study in Mathematics,
University of Madras,
Chennai - 600 005,
India.
ethandapani@yahoo.co.in

Abstract:

This paper is concerned with second-order linear noncanonical delay difference equations of the form

Δ(μ(t)Δ y(t))+ p(t)y(φ(t))=0.

The authors prove new oscillation criteria by first transforming the equation into canonical form and then obtaining some new monotonic properties of the positive solutions of the transformed equation. By using a comparison with first-order delay difference equations and a generalization of a technique developed by Koplatadze, they obtain their main results. Examples illustrating the improvement over known results in the literature are presented.

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