Local bifurcation analysis in nuclear reactor dynamics by Sotomayor’s theorem

Complexity Analysis of a Modified Predator-Prey System with Beddington–DeAngelis Functional Response and Allee-Like Effect on Predator

“…And a quintic algebraic equation of y * can be written in the form of q(y) ≔ 5 k�0 b k y k � 0 (see coefficients b k in Appendix A.2). Suppose that the denominator and numerator of expression (23) are all positive for some y * > 0; then, x * > 0. Notice that if b 5 > 0 and b 0 < 0, there must exist a positive root for the quintic equation…”

“…where J 22 � J 22 ( E (1) 2 ), r [PF] 1 ≔ m 1 + ((q 1 y 1 )/(a + cy 1 )). us, we have another theorem by using Sotomayor's theorem [22,23].…”

The Effects of Harvesting on the Dynamics of a Leslie–Gower Model

“…Lemma 2 (see [20,21]). Consider system _ X � f(X, α) and suppose that f(X 0 , α 0 ) � 0, n × n Jacobian matrix (J ≡ Df(X 0 , α 0 )) has a simple eigenvalue s � 0 with eigenvector V, and the transpose of the Jacobian matrix J T has an eigenvector W to the eigenvalue s � 0. en, the system _ X � f(X, α) experiences a transcritical bifurcation at the equilibrium point X 0 as the control parameter α passes through the bifurcation value α � α 0 if the following conditions are satisfied:…”

Effects of Immune Response and Time Delays in Models of Acute Myeloid Leukaemia

“…Ignacio et al showed that a key of the carcinogenic process is that the proliferation and differentiation of the LSC break away the inhibition feedback from terminally differentiated cells in the leukaemia lineage [25]. To control the output of multi-stage cell lineages, Lander et al studied different types of feedback configurations, feedback sensitivities [26,27] in the linages. For the treatment and prevention of the AML, Crowell et al regulated the feedback's strength among of the HSC, HPC and LSC [28,29].…”