Do the stability analysis of the following competing species system of equations with diffusion and advection
where V1 and V2 are advection velocities in x direction of the two populations with densities N1 and N2 respectively. a1 is the growth rate, b1 is the predation rate, d1 is the death rate, C1 is the conversion rate. D1 and D2 are diffusion coefficients. The initial and boundary conditions are:
at
and
where are the equilibrium solutions of the given system of equations.
Interpret the solution obtained and also write the limitations of the model.
___ __________ ________ ____ _________ _____ ___ _____ ___ ___ _______ ________.
________ ________ ____ __________ ___ ____ _______ _________ ___ ______ _________ _______.
________ __________ ________ _____ _______ ______ ___ ____ _______ __________ _______ ____.
_______ ____ ____ ____ _________ ________ ____ _____ _________.
________ _________ _________ _________ __________ ____ _________ _________.
__________ ____ ___ ______ ______ ______ ______.
____ ______ _______ ______ _____ ___ ___ ________ _________.
_______ ______ _____ ______ _____ _________.
____ ____ ______ _________ __________ __________ __________ ____ _____ ______.
___ ____ _____ ______ ____ __________ ________ ________ _______ _____ ____.
______ ____ _____ ________ ____ ______ __________ _____ _________ ____.
_____ _________ __________ ________ _________ ___ __________ ____.
________ _______ ___ __________ ____ __________ _________.
____ _______ ______ ________ ___ ______ ______ ___ ________ ________ _______ ______.
_________ ________ ____ ____ ____.
__________ ____ ________ _____ _______ _____.
_____ _______ ___ ___ _______ ____ _________.
________ ________ ____ _________ _____ ________ ___.
_____ ___ __________ _______ ________ ________ _____ ____ ______ ___.
___ _________ ______ ____ _______ ___ _________ __________ ________ ________ __________ __________.
_______ ____ __________ ______ _______ _____ ___ _______.
_________ ___ _______ ________ ____ _____.
______ __________ _____ ________ _____ _______ _____ _______ ________ _________.
__________ __________ ________ ______ __________ _____ ____ ______.
______ ________ _____ _____ ______ _______ ________ __________.
_____ _________ __________ _______ ____ ________ ____ _____ _______ ___.
_____ _____ _________ ____ _______ _____ ______.
_______ _________ _________ _______ _______ ____ ________ _____.
__________ ___ _______ _________ __________.
_________ _____ _________ _________ ___ ______ _____ _____ ___ _____ _____.
____ ___ _____ _________ __________ _____ ___ _____ ____ _________ ______ ___.
__________ ___ ________ ____ _____ ____ _____ __________.
_____ ______ _______ ______ _________ ___ _________ __________ ________.
_________ ______ ___ ___ _____ _________.
______ _____ ____ ________ __________ _____ ____ ___ _____ ________ ______ _____.
__________ _____ ________ _______ ______ _____ ______ _________ __________ _______ _________.
____ ___ _________ _________ _____ ____ _________ ____ _________.
_______ _____ ________ ____ _______ _____ ______ ___ _____ ___ __________ _______.
________ _______ ________ ____ ________ ____ ____ _____ ______ ____ ______.
____ ____ _____ _____ _________.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required
Let G(t) be the amount of the glucose in the bloodstream of a patient at time t. Assume that the glucose is infused into the bloodstream at a constant rate of . At the same time, the glucose is converted and removed from the bloodstream at a rate proportional to the amount of the glucose present. If at
then
i) formulate the model.
ii) find g(t) at any time t.
iii) discuss the long term behavior of the model.
Companies considering the purchase of a computer must first assess their future needs in order to determine the proper equipment. A computer scientist collected data from seven similar company sites so that computer hardware requirements for inventory management could be developed. The data collected is as follows:
| Customer Orders (in thousands) | Add-delete items (in thousands) | CPU time (in hours) |
| 123.5 | 2.108 | 141.5 |
| 146.1 | 9.213 | 168.9 |
| 133.9 | 1.905 | 154.8 |
| 128.5 | 0.815 | 146.5 |
| 151.5 | 1.061 | 172.8 |
| 136.2 | 8.603 | 160.1 |
| 92.0 | 1.125 | 108.5 |
The population consisting of all married couples is collected. The data showing the age of 12 married couples is as follows:
| Husband’s age (years) | Wife’s age (years) | Husband’s age (years) | Wife’s age (years) |
| 32 | 27 | 51 | 50 |
| 25 | 30 | 48 | 46 |
| 36 | 34 | 37 | 36 |
| 72 | 65 | 50 | 42 |
| 37 | 37 | 51 | 46 |
| 36 | 38 | 36 | 35 |
Return distributions of the two securities are given below:
| Return | Probabilities | |
| X | Y |
|
| 0.20 | 0.15 | 0.30 |
| 0.15 | 0.08 | 0.25 |
| 0.10 | 0.05 | 0.15 |
| 0.11 | 0.09 | 0.25 |
Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?
| Portfolio | Expected return | Standard deviation |
| W | 10% | 25% |
| X | 5% | 7% |
| Y | 17% | 37% |
| Z | 12% | 13% |
Ships arrive at a port at the rate of one in every 6 hours with exponential distribution of inter-arrival times. The time a ship occupies a berth for unloading has exponential distribution with an average of 12 hours. If the average delay of ships waiting for berths is to be kept below 15 hours, how many berths should be provided at the port?
A library wants to improve its service facilities in terms of the waiting time of its borrowers. The library has two counters at present and borrowers arrive according to Poisson distribution with arrival rate 2 every 10 minutes and service time follows exponential distribution with a mean of 15 minutes. The library has relaxed its membership rules and a substantial increase in the number of borrowers is expected. Find the number of additional counters to be provided if the arrival rate is expected to be twice the present value and the average waiting time of the borrower must be limited to half the present value.