Volume 8 (2019)  

1.  Dynamics of a diffusive Leslie-Gower predator-prey model with nonlinear prey harvesting  Full text (PDF)

R. Sivasamy, K. Sathiyanathan

Pages: 1-20

Abstract:  This paper considers a modified Leslie-Gower predator-prey model with Crowley-Martin functional response and nonlinear prey harvesting strategy subject to the no-flux boundary conditions. To understand the dynamics of the considered system, we derive sufficient conditions for permanence analysis, local stability, global stability and Hopf bifurcation of interior equilibrium point. Further we also investigate the existence and non-existence of non-constant positive steady state solutions. Finally numerical simulations are performed to verify the proposed theoretical results.

2.  Analysis of the multicellular converter with a cubic nonlinearity  Full text (PDF)

Philippe Djondiné

Pages: 21-28

Abstract:  This paper reports a two multicellular converter a smooth nonlinearity, described by a cubic polynomial. Some bifurcation phenomena and chaotic attractors observed and simulated by computer for the model are presented.

3.  Golden Ratios, Lucas Sequences and the Quadratic Family Full text (PDF)

Arturo Ortiz-Tapia

Pages: 29-37

Abstract:  It is conjectured that there is a converging sequence of some generalized Fibonacci ratios, given the difference between consecutive ratios, such as the golden ratio fi1 and the next golden ratio fi2. Moreover, the graphic depiction of those ratios shows some overlap with the quadratic family, and some numerical evidence suggests that all those ratios in the finite set obtained, belong to at least one quadratic family.