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Nonlinear Dynamical Systems
Inna Borodina, Professor, Russian Federation
Nonlinear dynamical systems can be linearized, if the relationship between elements of this is information.
To formalize the interaction between elements of the system it is important to know the nature of the phenomenon. Identify the main parameter of the process. Then the nonlinear of the system can be described as a characteristic of the environment. In every moment of life the environment system is described by constants. Nonlinear constants enable us to obtain linear equations system.
Linearization algorithm for dynamic system
1.Сonstruction structural model of the dynamic system.
2. The study of the nature of the processes taking place
3. The verbal description of the characteristics of the system
4. Creating a mathematical model of the popular tool is the system. Identifying the causes of non-linearity of the system (usually the cause is a positive feedback)
4. Description of conditions in which the system functioning
5. Creating a mathematical model, are popular tools of the system of linear differential equations
6. Identifying the causes of non-linearity of the system (typically, the impact of the environment)
7. Linearization is available if you imagine the behavior of a dynamical system in discrete time (the image - a stroboscopic effect)
8. Characteristics of the system change over time, changes can be studied quantitatively by means of differentiation,
9. In a separate, fixed point in time, we may assume that the system froze. This can be interpreted as the absence of nonlinearity (the image - stopped reel of film in one frame)
10. Covering all moments of life of the system - combine parts into a whole.
11.linear differential equations
dX1/dt=-X1(t)+...+Xn(t)+B1
..............................................
dXn/dt=-X1(t)+...-Xn(t)+Bn
Xi=parameters describing the behavior of the system
Bi=free coefficients are independent of time and describe the environment (nonlineare)
t= time
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Please E-mail Russian VersionMark Barkan, Consultant, United States Dear Inna, any chance you could e-mail the algorithm in Russian with an example of application. |
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Non Linear Dynamic SystemIvan Kohlinsky, Management Consultant, United Kingdom Inna - I read your 11 point method with interest. If I understand it correctly your are analyzing etc a non linear dynamic system by linearizing the non linear system using small discrete constructed/imaginary linear increments much in the way that a curve can be represented by very small increment straight lines and there is an analogy with differential calculus. I know that following the availability of high power digital computers and numerical analysis in the 1970s etc, non linear systems could and were studied and their outputs predicted using 'table look ups' of linear matrix type data. In the calculations. I would be interested to hear more about what sort of non linear systems you have been studying and applying this method to. |
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Response to Comments - Non Linear Dynamic System (Russian Version)Inna Borodina, Professor, Russian Federation Mark, Ivan! Forgive me for my bad English.
Ivan, you have correctly interpreted my writing.
I developed and used this is method for the analysis of advertising communication.
Ivan, Mark please send me an e-mail and I will send an article on Russian language. |
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Questions About Post on Nonlinear Dynamic SystemsAugusto Carreira, Partner, Portugal Inna, I found it difficult to understand the method just by this description. This seems quite interesting and worth looking further at it. Do you intend to publish a paper in English? It would be a major contribution. |
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Request for E-mail AddressMark Barkan, Consultant, United States Inna, here is my e-mail address: barkan@enecenter.com
Looking forward to your article. Thanks, Mark. |
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Answer About Paper in EnglishInna Borodina, Professor, Russian Federation Augusto, I'm afraid for a false expectation. For each particular system a long cognitive analysis is required. My research has been applied. The general methodology can be identified. In English version there is a presentation for a particular system and an overview of the study.
The question of placing the material to the administrator of the resource. Bids have been reported))). |
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Inna's Kind Offer of Article in RussianIvan Kohlinsky, Management Consultant, United Kingdom @ Inna Brodina: thank you for your kind offer of sending me a helpful explanatory article in Russian. Regrettably I would not have the ability to understand anything in the original Russian. Your English is good - it was good enough for me to understand what you meant, so do not worry. Maybe I spelt your surname incorrectly, but if this is you dancing between lectures then thats pretty impressive in this Utube clip www.youtube.com/watch?v=evV1lNIg63g |
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