Wright type delay differential equations with negative Schwarzian

We prove that the well-known $3/2$ stability condition established for the Wright equation (WE) still holds if the nonlinearity $p(\exp(-x)-1)$ in WE is replaced by a decreasing or unimodal smooth function $f$ with $f'(0)<0$ satisfying the standard negative feedback and below boundedness conditions and having everywhere negative Schwarz derivative.

[1]  J. Yorke Asymptotic stability for one dimensional differential-delay equations☆ , 1970 .

[2]  Viktor Tkachenko,et al.  A Global Stability Criterion for Scalar Functional Differential Equations , 2003, SIAM J. Math. Anal..

[3]  J. Mallet-Paret Morse Decompositions for delay-differential equations , 1988 .

[4]  Hans-Otto Walther,et al.  A theorem on the amplitudes of periodic solutions of differential delay equations with applications to bifurcation , 1978 .

[5]  R. Reissig A. D. Myschkis, Lineare Differentialgleichungen mit nacheilendem Argument (Hochschulbücher für Mathematik, Band 17). X + 181 S. m. 9 Abb. Berlin 1955. VEB Deutscher Verlag der Wissenschaften. Preis geb. 21,30 DM , 1960 .

[6]  W. D. Melo,et al.  ONE-DIMENSIONAL DYNAMICS , 2013 .

[7]  J. Guckenheimer ONE‐DIMENSIONAL DYNAMICS * , 1980 .

[8]  Hans-Otto Walther,et al.  Contracting return maps for monotone delayed feedback , 2001 .

[9]  W. Walter Differential and Integral Inequalities , 1970 .

[10]  A. Myshkis,et al.  Lineare Differentialgleichungen mit nacheilendem Argument , 1955 .

[11]  Chris Cosner,et al.  Book Review: Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems , 1996 .

[12]  Joseph W.-H. So,et al.  DIRICHLET PROBLEM FOR THE DIFFUSIVE NICHOLSON'S BLOWFLIES EQUATION , 1998 .

[13]  J. Hale Asymptotic Behavior of Dissipative Systems , 1988 .

[14]  E. M. Wright A non-linear difference-differential equation. , 1946 .

[15]  Hans-Otto Walther,et al.  The 2-dimensional attractor of x'(t)=-μx(t)+f(x(t-1)) , 1995 .

[16]  Eduardo Liz,et al.  Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima , 2002 .

[17]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[18]  John Mallet-Paret,et al.  A differential-delay equation arising in optics and physiology , 1989 .

[19]  E. M. Wright Linear difference-differential equations , 1948, Mathematical Proceedings of the Cambridge Philosophical Society.

[20]  Tibor Krisztin,et al.  Periodic Orbits and the Global Attractor for Delayed Monotone Negative Feedback , 1999 .

[21]  Tibor Krisztin,et al.  Unique Periodic Orbits for Delayed Positive Feedback and the Global Attractor , 2001 .

[22]  G. Sell,et al.  THE POINCARE-BENDIXSON THEOREM FOR MONOTONE CYCLIC FEEDBACK SYSTEMS WITH DELAY , 1996 .