A new approach for the analysis solution of dynamic systems containing fractional derivative

2006 ◽  
Vol 20 (5) ◽  
pp. 658-667 ◽  
Author(s):  
Dong-Pyo Hong ◽  
Young-Moon Kim ◽  
Ji-Zeng Wang
Keyword(s):  
Fractional Derivative ◽  
Dynamic Systems ◽  
New Approach

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

scholarly journals Une nouvelle approche pour immuniser nos forêts contre l'incertitude (essai)

2018 ◽  
Vol 169 (4) ◽  
pp. 199-202 ◽  
Author(s):  
Christian Messier ◽  
Fanny Maure ◽  
Núria Aquilué
Keyword(s):  
Forest Management ◽  
Global Change ◽  
Conceptual Framework ◽  
Complexity Theory ◽  
Dynamic Systems ◽  
Spatial Network ◽  
New Approach ◽  
The World ◽  
Present Context ◽  
Monitoring And Forecasting

A new approach to immunizing our forests against uncertainty (essay) In the present context of global change, managing our forests is a major challenge, in particular because of the great uncertainty associated with this change. Faced with this new reality, our methods of monitoring and forecasting the developments in our forests are no longer effective enough, so we have to review how we manage our forests. Complexity theory provides a conceptual framework for our approach, which leads us to adopt a more holistic and flexible way of seeing the world when planning our forest management. We must therefore accept that forests are complex and dynamic systems, and for that reason, never completely predictable. By incorporating the functional properties of trees and the complex spatial network of their populations in our forest management, and encouraging greater functional diversity and connectivity, we can immunize the forests against present and future stresses.

Developing a Multisemester Interwoven Dynamic Systems Project to Foster Learning and Retention of STEM Material

2004 ◽  
Author(s):  
Peter Avitabile ◽  
Stephen Pennell ◽  
John White
Keyword(s):  
Dynamic Systems ◽  
Basic Material ◽  
Mathematical Methods ◽  
Introductory Courses ◽  
New Approach ◽  
Science Technology ◽  
Educational Career ◽  
And Mathematics ◽  
Relationship Of ◽  
The Relationship

Students generally do not understand how basic STEM (Science, Technology, Engineering and Mathematics) material fits into all of their engineering courses. Basic material is presented in introductory courses but the relationship of the material to subsequent courses is unclear to the student since the practical relevance of the material is not necessarily presented. Students generally hit the “reset button” after each course not realizing the importance of basic STEM material. The capstone experience is supposed to “tie all the pieces together” but this occurs too late in the student’s educational career. A new multisemester interwoven dynamic systems project has been initiated to better integrate the material from differential equations, mathematical methods, laboratory measurements and dynamic systems across several semesters/courses so that the students can better understand the relationship of basic STEM material to an ongoing problem. This paper highlights the overall concept to be addressed by the new approach. The description of the project and modules under development are discussed.

scholarly journals Modeling the potential energy field caused by mass density distribution with Eton approach

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 106-113 ◽  
Author(s):  
Badr Saad T. Alkahtani ◽  
Abdon Atangana
Keyword(s):  
Potential Energy ◽  
Fractional Derivative ◽  
Mass Density ◽  
Variable Order ◽  
Modified Model ◽  
New Approach ◽  
Energy Field ◽  
Variable Order Derivative ◽  
With Memory ◽  
Real World Problems

AbstractA new approach for modeling real world problems called the “Eton Approach” was presented in this paper. The "Eton approach" combines both the concept of the variable order derivative together with Atangana derivative with memory derivative. The Atangana derivative with memory is used to account for the memory and fractional derivative for its filter effect. The approach was used to describe the potential energy field that is caused by a given charge or mass density distribution.We solve the modified model numerically and present supporting numerical simulations.

Structural Decomposition Approach for the Stability of Uncertain Dynamic Systems

1988 ◽  
Vol 55 (4) ◽  
pp. 992-994 ◽  
Author(s):  
Y. H. Chen ◽  
Chieh Hsu
Keyword(s):  
Dynamic Systems ◽  
A Priori ◽  
Parameter Variation ◽  
Stability Study ◽  
Fast Time ◽  
Time Varying ◽  
Decomposition Approach ◽  
New Approach ◽  
Uncertain Dynamic Systems ◽  
The Stability

The stability property for a class of dynamic systems with uncertain parameter variation is studied. The uncertainty can be fast time-varying and unpredictable. A new approach for stability study is proposed. The only required information on the uncertain variation is its possible bound as well as structure. That is, no a priori knowledge on the realization of the variation is needed.

New approach to fuzzy learning in dynamic systems

1989 ◽  
Vol 25 (12) ◽  
pp. 796 ◽  
Author(s):  
I.S. Shaw ◽  
J.J. Krüer
Keyword(s):  
Dynamic Systems ◽  
New Approach ◽  
Fuzzy Learning

scholarly journals Modeling and Application of a New Nonlinear Fractional Financial Model

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yiding Yue ◽  
Lei He ◽  
Guanchun Liu
Keyword(s):  
Interest Rate ◽  
Fractional Derivative ◽  
Empirical Model ◽  
Econometric Model ◽  
System Modeling ◽  
Financial System ◽  
Actual Data ◽  
Time Step ◽  
Financial Model ◽  
New Approach

The paper proposes a new nonlinear dynamic econometric model with fractional derivative. The fractional derivative is defined in the Jumarie type. The corresponding discrete financial system is considered by removing the limit operation in Jumarie derivative’s. We estimate the coefficients and parameters of the model by using the least squared principle. The new approach to financial system modeling is illustrated by an application to model the behavior of Japanese national financial system which consists of interest rate, investment, and inflation. The empirical results with different time step sizes of discretization are shown, and a comparison of the actual data against the data estimated by empirical model is illustrated. We find that our discrete financial model can describe the actual data that include interest rate, investment, and inflation accurately.

scholarly journals Antisystem-Approach (ASA) for Engineering of Wide Range of Dynamic Systems

2021 ◽  
Vol 3 (1) ◽  
pp. 52-66
Author(s):  
Serge Zacher
Keyword(s):  
Mathematical Model ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Chemical Engineering ◽  
Original System ◽  
New Approach ◽  
Analysis And Design ◽  
Wide Range ◽  
Newton’S Laws ◽  
Definition Of

Following the famous third physical Newton’s laws, “for every action there is an equal and opposite re-action”, a new approach for analysis and design of dynamic systems was introduced by [Zacher, 1997] and called «Antisystem-Approach» (ASA). According to this approach, a single isolated dynamic system does not exist alone. For every dynamic system, which transfers its inputs into outputs with an operator A in one direction, there is an equal system with the same operator A, which transfers other inputs into outputs in opposite direction. The antisystem does not have to be a physical system; it can also be a mathematical model of the original system. The most important feature of ASA is the exact balance between a system and its antisystem, which is called “energy” or “intensity”. In the group theory the system and antisystem are denote as antisymmetric. They build duality, which is common in many branches of sciences as mathematics, physics, biology etc. In the twenty years since first publication of the ASA there were developed different methods and applications, which enable to simplify the engineering, analysing the antisystem instead of original system. In the proposed paper is given the definition of ASA und are shown its features. It is described, how the ASA was used in electrical and chemical engineering, automation, informatics. Only several applications will be discussed, although ASA-solutions are common and could be used for wide range of dynamic systems.

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