Hopf bifurcation and stability analysis for a delayed equation with φ-Laplacian
DOI:
https://doi.org/10.12775/TMNA.2024.015Keywords
Functional-delay equations, Lyapunov-Krasovskii functional, stability, Hopf bifurcation, periodic solutionsAbstract
A formal framework for the analysis of Hopf bifurcations for a kind of delayed equation with $\varphi$-Laplacian and with a discrete time delay is presented, thus generalizing known results for the sunflower equation given by Somolinos in 1978. Also, under appropriate assumptions we prove the gradient-like behavior of the equation which, in turn, implies the non-existence of nonconstant periodic solutions. Our conditions improve previous results known in the literature for the standard case $\varphi(x)=x$.References
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Copyright (c) 2024 Pablo Amster, Mariel P. Kuna, Dionicio Santos
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