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 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.

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.

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.

Discrete Frequency Models: A New Approach to Temporal Analysis

2000 ◽  
Vol 123 (1) ◽  
pp. 98-103 ◽  
Author(s):  
Douglas E. Adams ◽  
Randall J. Allemang
Keyword(s):  
Dynamic Systems ◽  
Excitation Frequency ◽  
Temporal Analysis ◽  
Structural Vibrations ◽  
Single Degree Of Freedom ◽  
New Approach ◽  
Discrete Frequency ◽  
Nonlinear Responses ◽  
Vibration Responses ◽  
Continuous Frequency

Forced vibration responses of nonlinear systems contain harmonics of the excitation frequency. These harmonics are either directly forced or are subharmonic, superharmonic, or combination resonances. Nonlinear responses of this type have been modeled historically using continuous time, discrete time, and continuous frequency models. A new approach to dynamic systems analysis is introduced here that uses difference equations in the discrete frequency domain to describe the evolution of forced, single degree of freedom, steady state vibration responses in frequency instead of time. A variety of possible applications in nonlinear experimental structural vibrations are also discussed.

Stability Analysis of Uncertain Systems Using a Singular Value Decomposition-Based Metric

2015 ◽  
Vol 22 (05) ◽  
pp. 1550021 ◽  
Author(s):  
Young Kap Son ◽  
Gordon J. Savage
Keyword(s):  
Singular Value Decomposition ◽  
Dynamic Systems ◽  
Life Time ◽  
Singular Value ◽  
New Approach ◽  
Safety And Reliability ◽  
The Stability ◽  
Value Decomposition ◽  
Time Information ◽  
Domain Information

The stability of dynamic systems is important for satisfactory performance, safety and reliability. The study becomes more difficult when the system is nonlinear and when the ever present uncertainties in the components are considered. Herein a new approach is presented that uses time-domain information: It invokes design of experiments based on the uncertainty within the system, computer simulation of the dynamics to generate a matrix of discrete time responses that presents the variability of the response, and finally, singular value decomposition to separate out parameter information from time information. The variability in the elements in the first few left singular vectors predicts any instability that might occur over the complete life-time of the system. The key to the approach is the introduction of random variables and subsequent co-variance operations. A real-world example and comparison to established methods show the efficacy of the approach.

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