Consider a model for the dynamics of two interacting specise given by sestemot ODE dx =...

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Consider a model for the dynamics of two interacting specise given by sestemot ODE dx = 9- (b+1)x+x dt y dy = X- dt x(0)= x70, y(0) = y yo. where a,b, x 70. Determine the type of interaction between the speciese, is the system competitives or mutualistic or Predator-prey [Note: This may very depending on the population size]. You may assume without proof that the size of the populations remain strictly positive for all times. Determine the unique strictly positive steady state of the system. show that the stady state above is linearly asymptotically stable s a > (-1) b-1. Consider a model for the dynamics of two interacting specise given by sestemot ODE dx = 9- (b+1)x+x dt y dy = X- dt x(0)= x70, y(0) = y yo. where a,b, x 70. Determine the type of interaction between the speciese, is the system competitives or mutualistic or Predator-prey [Note: This may very depending on the population size]. You may assume without proof that the size of the populations remain strictly positive for all times. Determine the unique strictly positive steady state of the system. show that the stady state above is linearly asymptotically stable s a > (-1) b-1.