1,141 research outputs found
The Role of Constraints in a Segregation Model: The Symmetric Case
In this paper we study the effects of constraints on the dynamics of an
adaptive segregation model introduced by Bischi and Merlone (2011). The model
is described by a two dimensional piecewise smooth dynamical system in discrete
time. It models the dynamics of entry and exit of two populations into a
system, whose members have a limited tolerance about the presence of
individuals of the other group. The constraints are given by the upper limits
for the number of individuals of a population that are allowed to enter the
system. They represent possible exogenous controls imposed by an authority in
order to regulate the system. Using analytical, geometric and numerical
methods, we investigate the border collision bifurcations generated by these
constraints assuming that the two groups have similar characteristics and have
the same level of tolerance toward the members of the other group. We also
discuss the policy implications of the constraints to avoid segregation
Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems
We reinvestigate the dynamical behavior of a first order scalar nonlinear
delay differential equation with piecewise linearity and identify several
interesting features in the nature of bifurcations and chaos associated with it
as a function of the delay time and external forcing parameters. In particular,
we point out that the fixed point solution exhibits a stability island in the
two parameter space of time delay and strength of nonlinearity. Significant
role played by transients in attaining steady state solutions is pointed out.
Various routes to chaos and existence of hyperchaos even for low values of time
delay which is evidenced by multiple positive Lyapunov exponents are brought
out. The study is extended to the case of two coupled systems, one with delay
and the other one without delay.Comment: 34 Pages, 14 Figure
Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons
Multistability, the coexistence of multiple attractors in a dynamical system,
is explored in bursting nerve cells. A modeling study is performed to show that
a large class of bursting systems, as defined by a shared topology when
represented as dynamical systems, is inherently suited to support
multistability. We derive the bifurcation structure and parametric trends
leading to multistability in these systems. Evidence for the existence of
multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica
that is consistent with our proposed mechanism is presented. Although these
experimental results are preliminary, they indicate that single neurons may be
capable of dynamically storing information for longer time scales than
typically attributed to nonsynaptic mechanisms.Comment: 24 pages, 8 figure
Basins of attraction in nonsmooth models of gear rattle
This paper is concerned with the computation of the basins of attraction of a simple one degree-of-freedom backlash oscillator using cell-to-cell mapping techniques. This analysis is motivated by the modeling of order vibration in geared systems. We consider both a piecewise-linear stiffness model and a simpler infinite stiffness impacting limit. The basins reveal rich and delicate dynamics, and we analyze some of the transitions in the system's behavior in terms of smooth and discontinuity-induced bifurcations. The stretching and folding of phase space are illustrated via computations of the grazing curve, and its preimages, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit)
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