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On the global dynamics of the cancer AIDS-related mathematical model

Konstantin E. Starkov, Corina Plata-Ante (2014)

Kybernetika

In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive...

On the limit cycle of the Liénard equation

Kenzi Odani (2000)

Archivum Mathematicum

In the paper, we give an existence theorem of periodic solution for Liénard equation x ˙ = y - F ( x ) , y ˙ = - g ( x ) . As a result, we estimate the amplitude ρ ( μ ) (maximal x -value) of the limit cycle of the van der Pol equation x ˙ = y - μ ( x 3 / 3 - x ) , y ˙ = - x from above by ρ ( μ ) < 2 . 3439 for every μ 0 . The result is an improvement of the author’s previous estimation ρ ( μ ) < 2 . 5425 .

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