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.
The given discrete-time population model is represented by the equation:
\[ P_{n+1} = \frac{r P_n (K - P_n)}{K} + b \]
To find the steady-state, we set \(P_{n+1} = P_n = P\):
\[ P = \frac{r P (K - P)}{K} + b \]
Solving this equation for \(P\), we _____ ___ ____ _______ ___ ______.
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Consider the discrete time population model given by Nt+1=
for a population, where r is the intrinsic growth rated, b is a positive parameter. Determine the non-negative steady-state and discuss the linear stability of the model for 9 < r < .1 Also find the first bifurcation value of the parameters.
The daily capacity of each of the factory is 150 per day and the daily requirement over each target store is 200. Find the allocation for each factory to each target store which minimize the total transport cost.
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.
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Let ),t(P measured in kg, be the total mass or biomass of the fish population in a point at time t . Write the continuous model for the population growth using logistic equation. The intrinsic growth rate r and the carrying capacity k are given the values 70.0 per year and 6 80 7. ×10 kg respectively. If the initial biomass is P 25.0 0 = K, find the biomass after 2 years. Also find the time t , for which t(P ) 75.0 1 = K.
Consider the budworm population dynamics governed by the equation
where ,k the carrying capacity, and r, the birth rate of the budworm population, are positive parameters. Find out the steady states and use the perturbation to do the stability analysis of the equation for 0 < r < 1.
The yearly fluctuations in the groundwater table are believed to be dependent on the annual rainfall and the volume of water pumped out from the basin. The data collected on these variables for four consecutive years is given below:
Use the method of least squares to find a linear regression equation that best fits the data.