Lipschitz continuous dynamical system

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I stumbled upon the notion of a Lipschitz continuous dynamical system, and was wondering what this exactly meant. I guess it means that all solutions to (in my case the dynamical system is a set of ODE's) are Lipschitz continuous, but I wanted to be sure.

Thanks

dynamical-systems lipschitz-functions

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edited Jul 17 at 9:06

Bernard

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up vote
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I stumbled upon the notion of a Lipschitz continuous dynamical system, and was wondering what this exactly meant. I guess it means that all solutions to (in my case the dynamical system is a set of ODE's) are Lipschitz continuous, but I wanted to be sure.

Thanks

dynamical-systems lipschitz-functions

share|cite|improve this question

edited Jul 17 at 9:06

Bernard

110k635103

asked Jul 17 at 9:02

1233023

1398

add a comment | 

up vote
0
down vote

favorite

up vote
0
down vote

favorite

I stumbled upon the notion of a Lipschitz continuous dynamical system, and was wondering what this exactly meant. I guess it means that all solutions to (in my case the dynamical system is a set of ODE's) are Lipschitz continuous, but I wanted to be sure.

Thanks

dynamical-systems lipschitz-functions

share|cite|improve this question

edited Jul 17 at 9:06

Bernard

110k635103

asked Jul 17 at 9:02

1233023

1398

I stumbled upon the notion of a Lipschitz continuous dynamical system, and was wondering what this exactly meant. I guess it means that all solutions to (in my case the dynamical system is a set of ODE's) are Lipschitz continuous, but I wanted to be sure.

Thanks

dynamical-systems lipschitz-functions

share|cite|improve this question

edited Jul 17 at 9:06

Bernard

110k635103

asked Jul 17 at 9:02

1233023

1398

share|cite|improve this question

share|cite|improve this question

edited Jul 17 at 9:06

Bernard

110k635103

edited Jul 17 at 9:06

Bernard

110k635103

edited Jul 17 at 9:06

Bernard

110k635103

110k635103

asked Jul 17 at 9:02

1233023

1398

asked Jul 17 at 9:02

1233023

1398

asked Jul 17 at 9:02

1233023

1398

1398

add a comment | 

add a comment | 

1 Answer
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It means that the right side in $dot y=f(t,y)$ is Lipschitz-continuous in $y$. Then the uniqueness theorem applies (Picard-Lindelöf) and also numerical simulation will give meaningful results.

The solutions will be continuously differentiable, if the function $f$ is Lipschitz in all variables, then the solutions have (locally) Lipschitz continuous derivatives.

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edited Jul 17 at 9:41

answered Jul 17 at 9:33

LutzL

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote



accepted

It means that the right side in $dot y=f(t,y)$ is Lipschitz-continuous in $y$. Then the uniqueness theorem applies (Picard-Lindelöf) and also numerical simulation will give meaningful results.

The solutions will be continuously differentiable, if the function $f$ is Lipschitz in all variables, then the solutions have (locally) Lipschitz continuous derivatives.

share|cite|improve this answer

edited Jul 17 at 9:41

answered Jul 17 at 9:33

LutzL

49.8k31849

add a comment | 

up vote
1
down vote



accepted

It means that the right side in $dot y=f(t,y)$ is Lipschitz-continuous in $y$. Then the uniqueness theorem applies (Picard-Lindelöf) and also numerical simulation will give meaningful results.

The solutions will be continuously differentiable, if the function $f$ is Lipschitz in all variables, then the solutions have (locally) Lipschitz continuous derivatives.

share|cite|improve this answer

edited Jul 17 at 9:41

answered Jul 17 at 9:33

LutzL

49.8k31849

add a comment | 

up vote
1
down vote



accepted

up vote
1
down vote



accepted

It means that the right side in $dot y=f(t,y)$ is Lipschitz-continuous in $y$. Then the uniqueness theorem applies (Picard-Lindelöf) and also numerical simulation will give meaningful results.

The solutions will be continuously differentiable, if the function $f$ is Lipschitz in all variables, then the solutions have (locally) Lipschitz continuous derivatives.

share|cite|improve this answer

edited Jul 17 at 9:41

answered Jul 17 at 9:33

LutzL

49.8k31849

It means that the right side in $dot y=f(t,y)$ is Lipschitz-continuous in $y$. Then the uniqueness theorem applies (Picard-Lindelöf) and also numerical simulation will give meaningful results.

The solutions will be continuously differentiable, if the function $f$ is Lipschitz in all variables, then the solutions have (locally) Lipschitz continuous derivatives.

share|cite|improve this answer

edited Jul 17 at 9:41

answered Jul 17 at 9:33

LutzL

49.8k31849

share|cite|improve this answer

share|cite|improve this answer

edited Jul 17 at 9:41

edited Jul 17 at 9:41

edited Jul 17 at 9:41

answered Jul 17 at 9:33

LutzL

49.8k31849

answered Jul 17 at 9:33

LutzL

49.8k31849

answered Jul 17 at 9:33

LutzL

49.8k31849

49.8k31849

add a comment | 

add a comment | 

 

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