A chaotic system with only one stable equilibrium

If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is actually chaotic? Although chaos theory for three-dimensional autonomous systems has been intensively and extensively studied since the time of Lorenz in the 1960s, and the theory has become quite mature today, it seems that no one would anticipate a possibility of finding a three-dimensional autonomous quadratic chaotic system with only one stable equilibrium. The discovery of the new system, to be reported in this Letter, is indeed striking because for a three-dimensional autonomous quadratic system with a single stable node-focus equilibrium, one typically would anticipate non-chaotic and even asymptotically converging behaviors. Although the new system is not of saddle-focus type, therefore the familiar \v{S}i'lnikov homoclinic criterion is not applicable, it is demonstrated to be chaotic in the sense of having a positive largest Lyapunov exponent, a fractional dimension, a continuous broad frequency spectrum, and a period-doubling route to chaos.Comment: 13 pages, 10 figure

RESEARCH NEEDS IN AGRICULTURAL ECONOMICS FROM THE EXTENSION PERSPECTIVE: ATTITUDES VS. AN INVENTORY OF NEEDS

Teaching/Communication/Extension/Profession,

Biomarkers of Aging: From Primitive Organisms to Man

What biological changes take place as we age? Efforts by scientists to uncover the biomarkers of aging, that is, the normal phenomena of growing old, and to separate these inevitable physiologic changes from diseases and other factors.Warns that alleged "anti-aging" medicines like growth hormone injections are unprovable given current scientific knowledge

Periphere Mechanismen von Gelenkschmerzen mit speziellem Fokus auf den synovialen Fibroblasten

Zusammenfassung: Gelenkschmerz ist eine der am häufigsten auftretenden Schmerzformen. Etwa ein Drittel der Bevölkerung hat bereits einmal Gelenkschmerz erfahren. Bis heute ist diese Schmerzform nicht effektiv behandelbar, und Nebenwirkungen der verwendeten Medikamente sind häufig gefährlich. Es ist deshalb sehr wichtig, unser Verständnis über die Ursachen und die Mechanismen von Gelenkschmerzen weiter zu verbessern. Gelenke und ihre umgebenden Strukturen sind sehr gut mit Nervenfasern versorgt, die auf mechanische Beanspruchung reagieren. Lokale Entzündungsprozesse sensibilisieren diese Afferenzen, und es resultiert eine erniedrigte Schmerzschwelle. Über die lokalen Prozesse, insbesondere im Synovialgewebe, ist wenig bekannt. Rezeptoren, die im Nervensystem beschrieben sind, werden zunehmend auch im synovialen Fibroblasten nachgewiesen. Deren Funktion ist noch weitgehend unbekannt. Allerdings sind neue therapeutische Angriffspunkte über andere Systeme, z.B. den TRPV1- oder den P2X4-Rezeptor, zu erwarte

Signal buffering in random networks of spiking neurons: microscopic vs. macroscopic phenomena

In randomly connected networks of pulse-coupled elements a time-dependent input signal can be buffered over a short time. We studied the signal buffering properties in simulated networks as a function of the networks state, characterized by both the Lyapunov exponent of the microscopic dynamics and the macroscopic activity derived from mean-field theory. If all network elements receive the same signal, signal buffering over delays comparable to the intrinsic time constant of the network elements can be explained by macroscopic properties and works best at the phase transition to chaos. However, if only 20 percent of the network units receive a common time-dependent signal, signal buffering properties improve and can no longer be attributed to the macroscopic dynamics.Comment: 5 pages, 3 figure