I have a dynamical system that consists of three non-linear differential equations (dP/dt, dT/t, dN/dt). This system models a biological system. The system is so complicated that I have to use a numerical solver to find solutions en plot the bifurcation diagram. My problem is the following: I have written a code in Matlab to plot a bifurcation diagram. On the vertical axis I have a parameter a and on the horizontal axis a parameter b. I am interested in the stability of the fixed points. The steps in the code are as follows: Take a fixed point, for example: E=(P,T,0), so dP/dt=0, dT/dt=0, and N=0. 1. Start with a (a,b) from the grid. Plug this values in the system. Solve the corresponding system of equations for this fixed point. The solution is (P1,T1,0) 2. Test if the components are non-negative. If they are all non-negative then go to step 3. 3. Compute the Jacobian at E=(P1,T1,0). 4. Determine the eigenvalues. 5. If all the eigenvalues are negative, the equilibrium is stable for this combination (a,b).
The problem: Sometimes there are white regions in the diagram where Matlab does not plot anything. I think that this can means two things: 1. The solutions has a non-negative component. Or, 2. The equilibrium is unstable for this (a,b).
Someone explained to me that since the initial values are always positive, the solutions are always positive. This means that a system will always evolve towards a positive solution. So the system will not evolve towards a negative solution. This means that the white regions are unstable regions.
This is very confusing to me because solutions do have non-negative components sometimes, that’s why I build in the test. I don’t understand where I make a mistake in my thinking. I would really appreciate someone’s point of view.
✓ Extra quality
ExtraProxies brings the best proxy quality for you with our private and reliable proxies
✓ Extra anonymity
Top level of anonymity and 100% safe proxies – this is what you get with every proxy package
✓ Extra speed
1,ooo mb/s proxy servers speed – we are way better than others – just enjoy our proxies!
USA proxy location
We offer premium quality USA private proxies – the most essential proxies you can ever want from USA
Our proxies have TOP level of anonymity + Elite quality, so you are always safe and secure with your proxies
Use your proxies as much as you want – we have no limits for data transfer and bandwidth, unlimited usage!
Superb fast proxy servers with 1,000 mb/s speed – sit back and enjoy your lightning fast private proxies!
99,9% servers uptime
Alive and working proxies all the time – we are taking care of our servers so you can use them without any problems
No usage restrictions
You have freedom to use your proxies with every software, browser or website you want without restrictions
Perfect for SEO
We are 100% friendly with all SEO tasks as well as internet marketing – feel the power with our proxies
Buy more proxies and get better price – we offer various proxy packages with great deals and discounts
We are working 24/7 to bring the best proxy experience for you – we are glad to help and assist you!