what do the alpha, beta, and other variables represent. Would it be the growth rate and death rate of each animal?
@MikeSaintAntoine
4 ай бұрын
Hey Kealy, sorry about the late response but yes that's correct!
@christinag7924
10 ай бұрын
Both of the points at the end are steady states, right? or no?
@MikeSaintAntoine
9 ай бұрын
Hi Christina, sorry about the late response! Actually no -- this was a trick question and the points at the end are NOT steady states. One way to confirm this is to try plugging these points in to the ODE equations. In order for a point to be a steady state BOTH ODE equations need to equal zero, or else some change will be happening in the system. But if we plug these points in, we see that they cause one equation to be 0 and the other to be some number. So that's the mathematical way to check for steady states, but we can also reason about it logically to reach the same conclusion. For the first point, there is a positive number of the prey, and 0 predators. What would happen if this were the case? Well without any predators to kill the prey, the prey population would just keep increasing -- this means that change is happening in the system, so it isn't a steady state. For the second point, there are 0 prey and a positive number of predators. What would happen if this was the case? Well, without anything to eat, the predators would gradually die off -- this is a change happening in the system, which means that it isn't a steady state. So yeah, bit of a trick question! Thanks for watching and let me know if you have any questions! 🙂
@user-eh4sm7gz9p
8 ай бұрын
thank you so much for an amazing explanation.
@MikeSaintAntoine
8 ай бұрын
@@user-eh4sm7gz9p thanks for watching! 🙂
@arjunshah7105
4 ай бұрын
What's the answer lol
@MikeSaintAntoine
4 ай бұрын
Hey Arjun! The answer is that the points at the end are NOT steady states. One way to confirm this is to try plugging these points in to the ODE equations. In order for a point to be a steady state BOTH ODE equations need to equal zero, or else some change will be happening in the system. But if we plug these points in, we see that they cause one equation to be 0 and the other to be some number. So that's the mathematical way to check for steady states, but we can also reason about it logically to reach the same conclusion. For the first point, there is a positive number of the prey, and 0 predators. What would happen if this were the case? Well without any predators to kill the prey, the prey population would just keep increasing -- this means that change is happening in the system, so it isn't a steady state. For the second point, there are 0 prey and a positive number of predators. What would happen if this was the case? Well, without anything to eat, the predators would gradually die off -- this is a change happening in the system, which means that it isn't a steady state. Thanks for watching! 🙂
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