Dear all:
Recently, I want to do the bifurcation analysis of a model in following form:
ds/dt=b-ds-beta0(1+beta_1cos2pit)si;
di/dt=beta0(1+beta_1cos2pit)si-(gamma+d)i
dr/dt=gammai-dr
However, when I create the model in Matcont, the system will show the error, which shows that the virable "t" can not be identified.
Could someone tell me how to solve the problem?
I put both the model and error in the attachement.
Hello,
matcont treats only autonomous systems. There is a nice trick to make your system autonomous:
Add the two equations
co'=lambdaco - omegasi - (co^2 +si^2)co
si'=omegasi+lambdaco - (co^2+si^2)si
This system undergoes a supercritical Hopf bifurcation at lambda=0. If you follow the periodic solution until lambda=1, you obtain cos(omega t) and sin(omega t), quite likely with some phase shift, which doesn't matter here.
Good luck
Alois
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
If you just want to simulate, it suffices to select "numeric" ONLY for derivatives. You will find that your input was actually ok for that.
As soon as you want to do continuation, you will need an autonomous system. You can do that as indicated below.
From: Alois Steindl aloissteindl@users.sourceforge.net
Sent: Wednesday, October 20, 2021 5:38 PM
To: [matcont:discussion]
Subject: [matcont:discussion] how to create this model in Matcont?
Hello,
matcont treats only autonomous systems. There is a nice trick to make your system autonomous:
Add the two equations
co'=lambdaco - omegasi - (co^2 +si^2)co
si'=omegasi+lambdaco - (co^2+si^2)si
This system undergoes a supercritical Hopf bifurcation at lambda=0. If you follow the periodic solution until lambda=1, you obtain cos(omega t) and sin(omega t), quite likely with some phase shift, which doesn't matter here.
Good luck
Alois
Dear all:
Recently, I want to do the bifurcation analysis of a model in following form:
ds/dt=b-ds-beta0(1+beta_1cos2pit)si;
di/dt=beta0(1+beta_1cos2pit)si-(gamma+d)i
dr/dt=gammai-dr
However, when I create the model in Matcont, the system will show the error, which shows that the virable "t" can not be identified.
Could someone tell me how to solve the problem?
I put both the model and error in the attachement.
Hello,
matcont treats only autonomous systems. There is a nice trick to make your system autonomous:
Add the two equations
co'=lambdaco - omegasi - (co^2 +si^2)co
si'=omegasi+lambdaco - (co^2+si^2)si
This system undergoes a supercritical Hopf bifurcation at lambda=0. If you follow the periodic solution until lambda=1, you obtain cos(omega t) and sin(omega t), quite likely with some phase shift, which doesn't matter here.
Good luck
Alois
If you just want to simulate, it suffices to select "numeric" ONLY for derivatives. You will find that your input was actually ok for that.
As soon as you want to do continuation, you will need an autonomous system. You can do that as indicated below.
From: Alois Steindl aloissteindl@users.sourceforge.net
Sent: Wednesday, October 20, 2021 5:38 PM
To: [matcont:discussion]
Subject: [matcont:discussion] how to create this model in Matcont?
Hello,
matcont treats only autonomous systems. There is a nice trick to make your system autonomous:
Add the two equations
co'=lambdaco - omegasi - (co^2 +si^2)co
si'=omegasi+lambdaco - (co^2+si^2)si
This system undergoes a supercritical Hopf bifurcation at lambda=0. If you follow the periodic solution until lambda=1, you obtain cos(omega t) and sin(omega t), quite likely with some phase shift, which doesn't matter here.
Good luck
Alois
how to create this model in Matcont?
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