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In Section 2, we look at the admissible parameter regions and initial conditions for system (1).
Now in this section we present conditions for system (1.2) to be partially permanent and extinct.
And we obtain the sufficient conditions for system (1.3)'s permanence and balancing survival.
Figure 6 Sensitive dependence on the initial conditions for system ( 3 ).
However, by choosing σ as a bifurcation parameter, we obtain Hopf bifurcation conditions for system (1.2).
In this paper, our main purpose is to establish new results under new conditions for system (1.1).
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An approach is presented deriving analytical stability and bifurcation conditions for systems with periodically varying coefficients.
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Because of the specific nature of initial conditions for systems defined by means of Riemann-Liouville derivative, numerical example was given only for the systems with Caputo derivative.
The chaotic solution for σ < 0.028 corresponds to the observed turbulent film surface near flooding conditions for systems with upward gas flow.
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