( ) ( )

The characteristic equation of the matrix (3.9) has the form ( ) DetTrF +−= λλλ 2 , where “Tr” is the trace and “ Det ” is the determinant of the Jacobian matrix (3.9) which are given by

(3.11)

Since

Proof: Because

c) 01<−Det

1 2 2

2 2

Det e b b e p t d c c d p t

e b b e p t d c c d p t

α α α α

α α α α

− = + + − − + + −

⎡ ⎤ ⎡ ⎤+ + − − + − −⎣ ⎦ ⎣ ⎦ (3.14)

The conditions (b) and (c) defi ne a bounded region of stability in the parameters space ( )21 ,αα . Then the second and third conditions are the conditions for the local stability of equilibrium point which becomes: