3. Some populations (such as algae and bacteria) produce waste products, which in high concentrations are...

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3. Some populations (such as algae and bacteria) produce waste products, which in high concentrations are toxic to the population itself. A mathematical model for a population x(1) and a toxic waste product y(t) is dx =(a -B- Ky)x, %3D dt (5) dy = yx - Sy, dt where a, B, y, o and K are positive constants. (iv) Linearise the system near the steady states and determine their stability. Find the regions in parameter space such that the nontrivial (co-existence) equilibrium is a node or a spiral. [7 marks] 3. Some populations (such as algae and bacteria) produce waste products, which in high concentrations are toxic to the population itself. A mathematical model for a population x(1) and a toxic waste product y(t) is dx =(a -B- Ky)x, %3D dt (5) dy = yx - Sy, dt where a, B, y, o and K are positive constants. (iv) Linearise the system near the steady states and determine their stability. Find the regions in parameter space such that the nontrivial (co-existence) equilibrium is a node or a spiral. [7 marks]

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p ky z de dy yx sy dt For steady state ... View the full answer