Dynamics and Stability of Systems 

About: Dynamics and Stability of Systems is an academic journal. The journal publishes majorly in the area(s): Saddle-node bifurcation & Nonlinear system. Over the lifetime, 257 publications have been published receiving 4508 citations.

Hopf bifurcations in competitive three-dimensional Lotka-Volterra Systems

Abstract: We study the space of Lotka–Volterra systems modelling three mutually competing species, each of which, in isolation, would exhibit logistic growth. By a theorem of M. W. Hirsch, the compact limit sets of these systems are either fixed points or periodic orbits. We use a geometric analysis of the surfaces ẋ=0 of a system, to define a combinatorial equivalence relation on the space, in terms of simple inequalities on the parameters. We list the 33 stable equivalence classes, and show that in 25 of these classes all the compact limit sets are fixed points, so we can fully describe the dynamics. We study the remaining eight equivalence classes by finding simple algebraic criteria on the parameters, with which we are able to predict the occurrence of Hopf bifurcations and, consequently, isolated periodic orbits.

Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach

Abstract: We propose a discrete mapping to study the qualitative properties of the dynamics of biological or other complex networks, involving switchlike interactions between the various elements. The stable steady states and the limit cycles of the piecewise-linear equations which model such networks are derived from the dynamical behaviour of the proposed discrete mapping. Furthermore, this mapping takes into account not only the logical structure of the network but also the parameters used in the description.

Oscillatory behaviour in a three-component plankton population model

Abstract: We examine the qualitative behaviour of an NPZ (nutrient-phyto- plankton-zooplankton) model for parameter ranges consistent with values used in the literature. The wide range of values partly reflects variations of conditions in different environtments for the plankton, but in many cases is a measure of the difficulties in making observations and consequent uncertainties. We pay particular attention to the bifurcational behaviour of the system, and to the regions of parameter space for which oscillatory behaviour is possible; such oscillatory behaviour has recently been found in both observational data and in more complex ecosystem models. In some regions of parameter space, we also find that multiple attractors occur. Finally, we examine in more detail the behaviour for a range of values of nutrient input.

Efficiency, speed, and scaling of two-dimensional passive-dynamic walking

Abstract: We address performance limits and dynamic behaviours of the two dimensional passive-dynamic bipedal walking mechanisms of Tad McGeer. The results highlight the role of heelstrike in determining the mechanical efficiency of gait, and point to ways of improving efficiency. We analyse several kneed and straight-legged walker designs, with round feet and and point-feet. We present some necessary conditions on the walker mass distribution to achieve perfectly efficient (zero-slope-capable) walking for both kneed and straight-legged models. Our numerical investigations indicate, consistent with a previous study of a simpler model, that such walkers have two distinct gaits at arbitrarily small ground-slopes, of which the longer-step gait is stable at small slopes. Energy dissipation can be dominated by a term proportional to (speed) 2 from tangential foot velocity at heelstrike and from kneestrike, or a term proportional to (speed) 4 from normal foot collisions at heelstrike, depending on the gait, ground-slope,...

Stability results for impulsive differential systems with applications to population growth models

Abstract: This paper establishes some stability criteria for impulsive differential systems. It is shown that impulses do contribute to yield stability properties even when the corresponding differential system without impulses does not enjoy any stability behavior. As an application, these results are applied to some population growth models