Figure 6 Permanence of the infected prey I for models ( 1.1 ) and ( 1.2 ).
Many competitive systems have been studied recently by many authors and there is quite extensive literature concerned with the dynamics such as stability of equilibrium [2], persistence [3], permanence or partial extinction [4 7], positive periodic solution [8 11], positive almost periodic solution [12 15]etc.
Figure 7 Extinction of the infected prey I for model ( 1.2 ) when the two threshold values are (pmb{R^=1.0881>1}) and (pmb{R_=0.9982<1 }). Figure 8 Permanence of the infected prey I for model ( 1.2 ), the only difference between these graphs is the infection rate.
To enhance the effectiveness of the information being provided, risk communication messages should be designed so as to address five dimensions: (1) identity (i.e., what is the harm associated with the risk); (2) probability of risk occurring; (3) permanence of risk; (4) timing (i.e., when is it likely to occur); and (5) value (i.e., how much does the consequence matter) [ 41].
Specifically, the inclusion criterion for our study was based on the following definition of Holocaust survivor: an individual who had lived under Nazi rule or influence and was subject to: 1) forced displacement; 2) restriction in a ghetto; 3) permanence as a refugee or in hiding places; 4) confinement in forced labor camps or extermination camps [ 40].
VS has strong legal, ethical and political implications, with many questions remaining[61], including issues of diagnosis of VS with the medical and ethical imperative to keep a clear distinction between VS and the minimally conscious state [62], [63], establishing permanence, the decision to withdraw feeding, mode of death, and who best represents the patient's wishes.
See Figure 3. Figure 3 Stochastic permanence.
5, the permanence of (1.2) is discussed by some analytic techniques on limit sets of differential dynamical systems.
However, as is well known, the feedback control cannot influence the permanence [10, 21, 22, 24], therefore, the result not only improves but also supplements the known results.
Suppose that assumptions (H1), (H3) and (H5) hold, then the system (1.2) has permanence.
