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The global behavior of this equation is described in Section 8 and, in this case, every solution goes to infinity.
The results on the dynamics behavior of this equation and its modifications are abundant [3 21] and systematically collected and compared by Berezansky et al. [22].
This method is particularly efficient for numerical simulations of the granular gases equation with dissipative energy: it allows to study accurately the long time behavior of this equation and is very well suited for the study of clustering phenomena.
Monte Carlo simulations of the behavior of this equation were obtained using the publicly available software MesoRD 0.2.0 [ 33].
Since G is a g-partite graph with no edges between genes from the same organism, the number of edges m is: Thus, the upper bound of m grows with the quadratic term of g that dominates the behavior of this equation, and O(m) = O g).
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To the best of author's knowledge, nothing is known regarding the oscillatory behavior of the equation, so this article initiates the study.
The first one describes the asymptotic behavior of the equation.
The behavior of the equation is systematically explored and illustrated through numerical results.
As an application, we use the result to the study of an asymptotic behavior of that equation.
We can use this freedom to simplify the equation and reveal what the important parameters are that govern the behavior of the equation.
To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study.
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