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Two Multispecies Systems
Three Harvesting in Multispecies Systems
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assumed asymptotically behavior bioeconomic equilibrium bioeconomic model bioeconomic optimum biological characteristic equation Clark coexistence competing species Conrad considered constant harvesting control variables corresponding curves f defined differential equations dx/dt economic eigenvalues equilibrium point extinct Figure fishermen fishery fishing effort given growth rate Hamiltonian Hamiltonian function harvest rate integral curves interaction intersection interspecific competition isoclines Jacobian matrix Kolmogorov level of effort Lotka-Volterra mathematical maximize maximum principle Maximum Sustainable Yield MRAP necessary and sufficient necessary conditions obtain the system open access equilibrium open access problem optimal harvest P-P System parameter values parameters of Table positive predator is harvested Predator-Prey System prey population pristine system production function region Rescigno and Richardson revenue saddle point solution spiral sink stability analysis stability character sufficient conditions trajectory Transcritical Bifurcation type of stability Unstable Manifolds user cost values of Table vector yield effort curve