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 given discrete-time population model is \(N_{t+1} = rN_t \left(1 - \frac{N_t}{b}\right)\), where \(r\) is the intrinsic growth rate and \(b\) is a positive parameter. To analyze the steady-state and stability of the model, we set \(N_t = N_{t+1} = N^*\) and solve __________ ___ ________ _______ _______ _______ ___ ______ _______ ____ ___ _____.
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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 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.
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 locality is served by two malls. Each mall has two counters to serve the customers. Both the malls are equally popular and are known to have equal shares of the market. This is evident from the fact that customer’s arrive at each mall’s serving counter at the rate of 12 customers per hour. The average time to serve a customer is 05 minutes. Customers’ arrival is according to a Poisson distribution and the service time is exponential. To provide better service to the customers, the owners of the two malls decide to consolidate into a single larger mall. What is the effect of consolidation on the waiting time of customers?
A simple model including the seasonal change that affects the growth rate of a population is given by where C is a constant. If 0 x is the initial population, solve the equation and determine the maximum and minimum population.
Formulate the model for which the reproductive function of the cancer cells in the tumor surface is given by 2 1 ; c 1(2 c)2 3 c2 )c( ≠ − − φ = together with initial conditions 5 c = 20×10 at t = .0 Also find the density of the cancer cells in the tumour’s surface area at t = 20 days.
The transportation cost of 600 tons of a certain type of material from four factories B1, B2 , B3 , and B4 to three target stores T1,T2 , and T3 are given in the following table:
