The Latka-Volterra predator-prey model consists of two equations and three parameters. By first assigning random values to the three parameters, and then comparing the resulting data to a second set of data, we wish to recover the parameters used to form the second set of data. In order to do thi... Show moreThe Latka-Volterra predator-prey model consists of two equations and three parameters. By first assigning random values to the three parameters, and then comparing the resulting data to a second set of data, we wish to recover the parameters used to form the second set of data. In order to do this, we calculate the difference, or cost, between the two sets of data and minimize the cost using an optimization routine which utilizes a gradient technique.The optimization routine will recover the correct combination of the three parameters that can replicate the second data set only if it can find the globally minimum in the cost function. However, there are many locally minimum that sidetrack the optimizer. When it finds one of these local minimums, the optimizer returns an incorrect combination of the three parameters. Our experiment confirmed that although the optimizer would find most often find local minimums, it did find global minimums 14-30% of the time. Therefore recovering parameters using a gradient technique is effective at fitting a model to data. We are able to reduce the number of local minimums by adding parameter weights to our cost function. A second experiment revealed that, with parameter weights, the global minimum was found 18-30% of the time. Show less
