We provide sufficient conditions for existence of viable solutions of fractional differential inclusions with Caputo derivative and fraction order 0 < q < 1, correcting the results of [9,11].
The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability are investigated. On the other hand, it is demonstrated that the model endures Hopf bifurcation about its positive steady-state when the growth rate of the consumer is selected as a bifurcation parameter. Bifurcating and chaotic behaviors are controlled through the implementation of chaos control strategies. In the end, all mathematical discussion, especially Hopf bifurcation, methods related to the control of chaos and global asymptotic stability for a positive steady-state, is supported with suitable numerical simulations.
A topological index is a numerical number associated with a graph that describes its topology. History traces a long path on the study of topological indices. A circulant graph is one of the most comprehensive families, as its specializations give some important families like complete graphs, crown graphs, rook graphs, complete bipartite graphs, cocktail party graphs, empty graphs, etc. The aim of this report is to compute the first and second K Banhatti indices of circulant graph. We also compute the first and second K hyper Banhatti indices of this family of graph. Moreover, we plot our results to see the dependences of the first and second K Banhatti indices and the first and second K hyper Banhatti indices on the involved parameters.
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