The delayed Duffing equation $${\ddot{x}}(t)+x(t-T)+x^3(t)=0$$ is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions, for fixed delays such that $$T^2<\tfrac{3}{2}\pi ^2$$ . In contrast several previous works which involved approximate the treatment here exact.

The UCLA Academic Senate has completed its review of the UCPB Paper on Differential Fees and Nonresident Tuition. The proposal has been reviewed by our Council on Planning and Budget (CPB), Graduate Council, Undergraduate Council, Committee on Undergraduate Admissions and Relations with Schools, and numerous Faculty Executive Committees (School of Arts and Architecture, School of Theater, Film,...

We study the dynamics near transverse intersections of stable and unstable manifolds of sheets of symmetric periodic orbits in reversible systems. We prove that the dynamics near such homoclinic and heteroclinic intersections is not C1 structurally stable. This is in marked contrast to the dynamics near transverse intersections in both general and conservative systems, which can be C1 structura...

An analytical model for the soil carbon and nitrogen cycles is studied from the dynamical system point of view. Its main nonlinearities and feedbacks are analyzed by considering the steady state solution under deterministic hydro-climatic conditions. It is shown that, changing hydroclimatic conditions, the system undergoes dynamical bifurcations, shifting from a stable focus to a stable node an...

Models reveal that sexually antagonistic co-evolution exaggerates female resistance and male persistence traits. Here we adapt an established model by including directional sexual selection acting against persistence. We find similar equilibria to previous models showing that sexually antagonistic co-evolution can be limited by counteracting sexual, as well as, natural selection. We tested the ...

Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with a focus on multistability, limit cycles and limit cycle bifurcations. The results are then used for construction of two reaction systems, which are at the deterministic level described by twodimensional third-degree kinetic ODEs. The first syst...

This study elucidates the origin of the multiplicity of stable oscillatory flows detected by time integration in tall rectangular cavities heated from the side. By using continuation techniques for periodic orbits, it is shown that initially unstable branches, arising at Hopf bifurcations of the basic steady flow, become stable after crossing Neimark-Sacker points. There are no saddle-node or p...