Do the stability analysis of the trivial equilibrium solution of the following competing species model:
where D1 and D2 are diffusion coefficients of the two population densities N1 and N , 2 respectively. 1 a is the growth rate, 1 b is the predation rate, 1 d is the death rate and 1 c is the conversion rate. The initial boundary conditions are
where Ni are the equilibrium solutions of the given system of equations.
To perform the stability analysis of the trivial equilibrium solution of the given competing species model, we start by considering the equilibrium solution where both population densities \(N_1\) and \(N_2\) are constant. Let these equilibrium values be denoted by \(N_{1e}\) and \(N_{2e}\). Substituting these values into the system of equations and setting the derivatives equal to zero, we get:
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The deviation )t(g of a patient’s blood glucose concentration from its optimal concentration satisfies the differential equation
for α being a positive constant, immediately after the patient fully absorbs a large amount of glucose. The time t is measured in minutes. Identify the type (over-damped, under-damped or critically-damped) of this differential equation. Find the condition on α for which the patient is normal.
Ships arrive at a port at the rate of one in every 4 hours, with exponential distribution of inter-arrival times. The time a ship occupies a berth for unloading has exponential distribution with an average of 10 hours. If the average delay of ships waiting for berths is to be kept below 14 hours, how many berths should be provided at the port?
Consider the discrete time population model given
where K is the carrying capacity of the population, r is the intrinsic growth rate and b is a positive parameter. Determine the non-negative steady-state and discuss the linear stability of the model for 0 < r < .1 Also find the first bifurcation value of a the parameter r.
A company has three factories F1 ,F2 F 3, and these factories supply to three markets M1 , M2 , M3 . The transportation costs from each factory to each market are given in the table. Capacities ‘ i a ’ s’ of the factories and market requirements ‘ bj ’s’ are also shown in the table. Find the minimum transportation cost.
Ships arrive at a port at the rate of one in every 4 hours with exponential distribution of inter arrival times. The time a ship occupies a berth for unloading has exponential distribution with an average of 10 hours. If the average delay of ships waiting for a berth is to be kept below 14 hours, how many berths should be provided at the port?
The return distribution on the two securities X and Y are given in the table below:
| Possible Rates of Return | Associated Probability | |
| X | Y | Pxj=Pyj |
| 0.10 | 0.09 | 0.20 |
| 0.11 | 0.11 | 0.22 |
| 0.17 | 0.16 | 0.25 |
| 0.19 | 0.18 | 0.33 |
Find
Consider the data showing observations on the quantity demanded of a certain commodity depending on commodity price and consumers’ income:
Find the multiple regression equation that best fits the data.