Nonlinear Dynamical Systems

System Dynamics & Systems Thinking
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Inna Borodina
Russian Federation

Nonlinear Dynamical Systems

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

  Mark Barkan, United States
 

Please E-mail Russian Version

Dear Inna, any chance you could e-mail the algorithm in Russian with an example of application....

  Ivan Kohlinsky
Management Consultant, United Kingdom
 

Non Linear Dynamic System

Inna - I read your 11 point method with interest. If I understand it correctly your are analyzing etc a non linear dynam...

  Inna Borodina
Russian Federation
 

Response to Comments - Non Linear Dynamic System (Russian Version)

Mark, Ivan! Forgive me for my bad English. Ivan, you have correctly interpreted my writing. I developed and used this ...

  Augusto Carreira
Partner, Portugal
 

Questions About Post on Nonlinear Dynamic Systems

Inna, I found it difficult to understand the method just by this description. This seems quite interesting and worth loo...

  Mark Barkan, United States
 

Request for E-mail Address

Inna, here is my e-mail address: barkan@enecenter.com Looking forward to your article. Thanks, Mark....

  Inna Borodina
Russian Federation
 

Answer About Paper in English

Augusto, I'm afraid for a false expectation. For each particular system a long cognitive analysis is required. My resear...

  Ivan Kohlinsky
Management Consultant, United Kingdom
 

Inna's Kind Offer of Article in Russian

@Inna Brodina: thank you for your kind offer of sending me a helpful explanatory article in Russian. Regrettably I would...

 

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