Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters

By Edoardo Beretta, Yang Kuang. SIAM Journal on Mathematical Analysis, 2002

636 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Genetics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/786c37d0843373f17ec91ac0e0bbbc03c9db17fa

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Citations in the corpus

Geometric stability switch criteria in delay differential equations with two delays and delay dependent parameters (2019, methodology): “An), e.beretta@mat.uniurb.it (E. Beretta), kuang@asu.edu (Y. Kuang), wangchuncheng@hit.edu.cn (C. Wang), hao8@ualberta.ca (H. Wang). https://doi.org/10.1016/j.jde.2018.11.025 0022-0396/© 2018 Elsevier Inc.”
On stability crossing curves for general systems with two delays (2004, background): “Another interesting study on such switches was conducted recently by Beretta and Kuang [2] regarding systems whose coefficients depend on the delays.”
On the zeros of transcendental functions with applications to stability of delay differential equations with two delays (2003, methodology): “studied the second degree exponential polynomials; Ruan [41] studied the distribution of zeros of some second order exponential polynomials and used the results to investigate the stability and bifurcations in Kolmogorov types of predatorprey systems, see also Martin and Ruan [33]; Ruan and Wei [42]”
Bifurcation analysis in a time-delay model for prey–predator growth with stage-structure (2007, methodology): “Equation (7) takes the form of a second-degree exponential polynomial in λ, with all the coefficients of P and Q depending on τ . Beretta and Kuang [ 4 ] established a geometrical criterion which gives the existence of purely imaginary roots of a characteristic equation with delay-dependant coeffici”
Wavefronts and global stability in a time-delayed population model with stage structure (2003, background): “…rate is constant, as in the Nicholson's blow®ies model, then the dynamics is more colourful and qualitatively dependent on the time delay (positive steady state, if it exists, may be stable for both small and large delay, and unstable for intermediate delay (see Beretta & Kuang 2002; Cooke et al .”
Stability and global Hopf bifurcation in toxic phytoplankton–zooplankton model with delay and selective harvesting (2013, methodology): “Thus, we use the method introduced by Beretta and Kuang [26], which gives the existence of purely imaginary roots of a characteristic equation with delaydependent coefficients (see also [27, 28]).”
A dynamic IS-LM model with delayed taxation revenues (2005, background): “Therefore (see [ 3 ]) a pair of pure imaginary roots k =± ix cross the imaginary axis from left to right if dRekðh”