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! 🙂
Hi, sorry about the confusion! I put on the plot axis label that the unit here is in the hundreds, so the predator population was starting at 1 (hundred) and the prey population was starting at 10 (hundred). But I forgot to actually say this! So good point, yes if it was just one predator then it wouldn't make sense because they would't be able to reproduce.
@@MikeSaintAntoine if x=initial number of predators and y=initial number of prey do we always start by getting to a situation where x=1? it seems that this makes the calculations easier because x*y=y, am I thinking correctly?
@@ciferusbux Note that the values of x and y in this model are not necessarily integers. For example, x could be 327.61325.... The model isn't meant to provide an exact number of predator/prey at a certain time, it is meant to demonstrate the overall trends in the population change over time. Hopefully that helps.
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! 🙂
Both of the points at the end are steady states, right? or no?
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! 🙂
thank you so much for an amazing explanation.
@@ايماناللبدي-ب4ع thanks for watching! 🙂
the population status of the predator is 1, that's a bit strange, will it reproduce? I'm asking seriously
Hi, sorry about the confusion! I put on the plot axis label that the unit here is in the hundreds, so the predator population was starting at 1 (hundred) and the prey population was starting at 10 (hundred). But I forgot to actually say this! So good point, yes if it was just one predator then it wouldn't make sense because they would't be able to reproduce.
@@MikeSaintAntoine if x=initial number of predators and y=initial number of prey do we always start by getting to a situation where x=1?
it seems that this makes the calculations easier because x*y=y, am I thinking correctly?
@@ciferusbux Note that the values of x and y in this model are not necessarily integers. For example, x could be 327.61325.... The model isn't meant to provide an exact number of predator/prey at a certain time, it is meant to demonstrate the overall trends in the population change over time. Hopefully that helps.
what do the alpha, beta, and other variables represent. Would it be the growth rate and death rate of each animal?
Hey Kealy, sorry about the late response but yes that's correct!
What's the answer lol
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! 🙂