Search results for "Stable equilibrium"
showing 5 items of 5 documents
A Cointegration Analysis of Car Advertising and Sales Data in the Presence of Structural Change
2006
Abstract This paper examines whether there is a long‐run stable equilibrium relationship between advertising and sales across the market segments of the UK car industry over the period 1971–2001. In order to achieve this goal, we allow for structural breaks in the series using cointegration techniques. The results show the existence of long‐run equilibrium relationships in all six market segments, although in four of them the relationship is not stable. In general, one structural change is detected in the late 1970s and another in the early 1990s, coinciding with two economic recessions. When we do not account for structural changes, the estimated long‐run elasticities of advertising on sal…
Hidden Oscillations in Electromechanical Systems
2016
In this paper an electromechanical system with two different types of motor is considered. It is shown that during the spin-up, the system with DC motor may experience unwanted vibration—the Sommerfeld effect. This is a well-known effect when the motor of electromechanical system gets stuck near the resonance zone instead of reaching its nominal power. The absence of this effect is demonstrated in the system with synchronous motor. Nowadays, there are many works devoted to the study of this effect in various systems. Here we discuss the Sommerfeld effect from the point of view of localization of the so-called hidden oscillations.
Characterizing the Phase Transitions between Stable Equilibrium and Periodic Oscillations in Predator-prey Population Dynamics: A Theoretical Apprais…
2020
Multi-phase patterns with more or less sharp phase transitions, first highlighted in thermodynamics, have progressively revealed having wider relevance, being encountered in various other contexts, for example fluid mechanics, and can even occur in the interactive dynamics in biological populations involving two or more species that share opposite interests, such as predator-prey or parasite-host pairs of species. In the latter, the pattern of abundances of both interacting species usually reaches an equilibrium level which can be either stable or cyclic (with large periodic oscillations in the latter case). Both alternative modes are separated by well-define boundaries and, accordingly, ca…
Separatrix reconstruction to identify tipping points in an eco-epidemiological model
2018
Many ecological systems exhibit tipping points such that they suddenly shift from one state to another. These shifts can be devastating from an ecological point of view, and additionally have severe implications for the socio-economic system. They can be caused by overcritical perturbations of the state variables such as external shocks, disease emergence, or species removal. It is therefore important to be able to quantify the tipping points. Here we present a study of the tipping points by considering the basins of attraction of the stable equilibrium points. We address the question of finding the tipping points that lie on the separatrix surface, which partitions the space of system traj…
Competitive selection in mono-, di- and tri-genotype cultures of Drosophila melanogaster
2009
Viability and larva-to-adult development of three strains of Drosophila melanogaster (one wild strain and two eye mutant strains: cardinal and sepia) were studied under three different situations: A. Monocultures of wild, cardinal and sepia respectively. B. Dicultures with the combinations wild/cardinal, wild/sepia and cardinal/sepia respectively. Seven points of different genetical composition were chosen for each of the three systems. C. Tricultures with wild/cardinal/sepia. Seventy composition points were chosen. The points arranged in a three dimensional diagram with the axes wild, cardinal and sepia, make up an equilateral triangle hyperplane. An analysis of optimal density and intrins…