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What are 'branches of equilibria' and 'branch points'?
The Next CEO of Stack Overflowbirth-death models, equilibria and stabilityDifferential Equations reference for Putnam preparationPractical applications of first order exact ODE?Equilibria and stabilityFinding equilibria and stabilityFinding equilibria and determining their behaviourVon Bertalanffy model of tumor growth and Gompertz model - equilibria and stabilityNext generation matrix for virus dynamic modelWhat is the rigorous definition of $dy$ and $dx$?Reference Request: Getting from introductory PDEs to kinetic models, non-local aggregation, and mean field games
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I'm reading through an article which proposes a population interaction model for treating cancer with viral therapy with differential equations and in the bifurcation analysis they have mentioned these two concepts multiple times. I've never heard of them and I couldn't find them in any of the books I looked through.
Can anyone help out in explaining to me these concepts?
ordinary-differential-equations mathematical-modeling
asked Mar 28 at 0:40
D. BritoD. Brito
385111
$endgroup$
add a comment |
$begingroup$
I'm reading through an article which proposes a population interaction model for treating cancer with viral therapy with differential equations and in the bifurcation analysis they have mentioned these two concepts multiple times. I've never heard of them and I couldn't find them in any of the books I looked through.
Can anyone help out in explaining to me these concepts?
ordinary-differential-equations mathematical-modeling
asked Mar 28 at 0:40
D. BritoD. Brito
385111
$endgroup$
1
$begingroup$
If you pick a point in parameter space and find some equilibrium in phase space, what happens when you change one of the parameter after that? If you picked an equilibrium with no zero eigenvalues in its linearization, it will just change its position in phase space tracing some smooth curve. However, what happens when equilibrium has zero eigenvalue? It could be a saddle-node bifurcation, where two distinct branches of equilibria intersect at branch point and might cease to exist afterwards. Also, take a look at Doedel's lectures.
$endgroup$
– Evgeny
Mar 28 at 16:09
add a comment |
$begingroup$
I'm reading through an article which proposes a population interaction model for treating cancer with viral therapy with differential equations and in the bifurcation analysis they have mentioned these two concepts multiple times. I've never heard of them and I couldn't find them in any of the books I looked through.
Can anyone help out in explaining to me these concepts?
ordinary-differential-equations mathematical-modeling
asked Mar 28 at 0:40
D. BritoD. Brito
385111
$endgroup$
I'm reading through an article which proposes a population interaction model for treating cancer with viral therapy with differential equations and in the bifurcation analysis they have mentioned these two concepts multiple times. I've never heard of them and I couldn't find them in any of the books I looked through.
Can anyone help out in explaining to me these concepts?
ordinary-differential-equations mathematical-modeling
ordinary-differential-equations mathematical-modeling
asked Mar 28 at 0:40
D. BritoD. Brito
385111
asked Mar 28 at 0:40
D. BritoD. Brito
385111
asked Mar 28 at 0:40
D. BritoD. Brito
385111
asked Mar 28 at 0:40
D. BritoD. Brito
385111
asked Mar 28 at 0:40
D. BritoD. Brito
385111
385111
1
$begingroup$
If you pick a point in parameter space and find some equilibrium in phase space, what happens when you change one of the parameter after that? If you picked an equilibrium with no zero eigenvalues in its linearization, it will just change its position in phase space tracing some smooth curve. However, what happens when equilibrium has zero eigenvalue? It could be a saddle-node bifurcation, where two distinct branches of equilibria intersect at branch point and might cease to exist afterwards. Also, take a look at Doedel's lectures.
$endgroup$
– Evgeny
Mar 28 at 16:09
add a comment |
1
$begingroup$
If you pick a point in parameter space and find some equilibrium in phase space, what happens when you change one of the parameter after that? If you picked an equilibrium with no zero eigenvalues in its linearization, it will just change its position in phase space tracing some smooth curve. However, what happens when equilibrium has zero eigenvalue? It could be a saddle-node bifurcation, where two distinct branches of equilibria intersect at branch point and might cease to exist afterwards. Also, take a look at Doedel's lectures.
$endgroup$
– Evgeny
Mar 28 at 16:09
1
1
$begingroup$
If you pick a point in parameter space and find some equilibrium in phase space, what happens when you change one of the parameter after that? If you picked an equilibrium with no zero eigenvalues in its linearization, it will just change its position in phase space tracing some smooth curve. However, what happens when equilibrium has zero eigenvalue? It could be a saddle-node bifurcation, where two distinct branches of equilibria intersect at branch point and might cease to exist afterwards. Also, take a look at Doedel's lectures.
$endgroup$
– Evgeny
Mar 28 at 16:09
$begingroup$
If you pick a point in parameter space and find some equilibrium in phase space, what happens when you change one of the parameter after that? If you picked an equilibrium with no zero eigenvalues in its linearization, it will just change its position in phase space tracing some smooth curve. However, what happens when equilibrium has zero eigenvalue? It could be a saddle-node bifurcation, where two distinct branches of equilibria intersect at branch point and might cease to exist afterwards. Also, take a look at Doedel's lectures.
$endgroup$
– Evgeny
Mar 28 at 16:09
add a comment |
0
active
oldest
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If you pick a point in parameter space and find some equilibrium in phase space, what happens when you change one of the parameter after that? If you picked an equilibrium with no zero eigenvalues in its linearization, it will just change its position in phase space tracing some smooth curve. However, what happens when equilibrium has zero eigenvalue? It could be a saddle-node bifurcation, where two distinct branches of equilibria intersect at branch point and might cease to exist afterwards. Also, take a look at Doedel's lectures.
$endgroup$
– Evgeny
Mar 28 at 16:09