9 research outputs found
A nontwist field line mapping in a tokamak with ergodic magnetic limiter
For tokamaks with uniform magnetic shear, Martin and Taylor have proposed a
symplectic map has been used to describe the magnetic field lines at the plasma
edge perturbed by an ergodic magnetic limiter. We propose an analytical
magnetic field line map, based on the Martin-Taylor map, for a tokamak with
arbitrary safety factor profile. With the inclusion of a non-monotonic profile,
we obtain a nontwist map which presents the characteristic properties of
degenerate systems, as the twin islands scenario, the shearless curve and
separatrix reconnection. We estimate the width of the islands and describe
their changes of shape for large values of the limiter current. From our
numerical simulations about the shearless curve, we show that its position and
aspect depend on the control parameters
Identification of single- and double-well coherence-incoherence patterns by the binary distance matrix
The study of chimera states or, more generally, coherence-incoherence
patterns has led to the development of several tools for their identification
and characterization. In this work, we extend the eigenvalue decomposition
method to distinguish between single-well and double-well patterns. By applying
our method, we are able to identify the following four types of dynamical
patterns in a ring of nonlocally coupled Chua circuits and nonlocally coupled
cubic maps: single-well cluster, single-well coherence-incoherence pattern,
double-well cluster, and double-well coherence-incoherence. In a ring-star
network of Chua circuits, we investigate the influence of adding a central node
on the spatio-temporal patterns. Our results show that increasing the coupling
with the central node favors the occurrence of single-well
coherence-incoherence states. We observe that the boundaries of the attraction
basins resemble fractal and riddled structure
Fractional dynamics and recurrence analysis in cancer model
In this work, we analyze the effects of fractional derivatives in the chaotic
dynamics of a cancer model. We begin by studying the dynamics of a standard
model, {\it i.e.}, with integer derivatives. We study the dynamical behavior by
means of the bifurcation diagram, Lyapunov exponents, and recurrence
quantification analysis (RQA), such as the recurrence rate (RR), the
determinism (DET), and the recurrence time entropy (RTE). We find a high
correlation coefficient between the Lyapunov exponents and RTE. Our simulations
suggest that the tumor growth parameter () is associated with a chaotic
regime. Our results suggest a high correlation between the largest Lyapunov
exponents and RTE. After understanding the dynamics of the model in the
standard formulation, we extend our results by considering fractional
operators. We fix the parameters in the chaotic regime and investigate the
effects of the fractional order. We demonstrate how fractional dynamics can be
properly characterized using RQA measures, which offer the advantage of not
requiring knowledge of the fractional Jacobian matrix. We find that the chaotic
motion is suppressed as decreases, and the system becomes periodic for
. We observe limit cycles for and fixed points for . The fixed point is
determined analytically for the considered parameters. Finally, we discover
that these dynamics are separated by an exponential relationship between
and . Also, the transition depends on a supper transient which
obeys the same relationship
Unpredictability in seasonal infectious diseases spread
In this work, we study the unpredictability of seasonal infectious diseases
considering a SEIRS model with seasonal forcing. To investigate the dynamical
behaviour, we compute bifurcation diagrams type hysteresis and their respective
Lyapunov exponents. Our results from bifurcations and the largest Lyapunov
exponent show bistable dynamics for all the parameters of the model. Choosing
the inverse of latent period as control parameter, over 70% of the interval
comprises the coexistence of periodic and chaotic attractors, bistable
dynamics. Despite the competition between these attractors, the chaotic ones
are preferred. The bistability occurs in two wide regions. One of these regions
is limited by periodic attractors, while periodic and chaotic attractors bound
the other. As the boundary of the second bistable region is composed of
periodic and chaotic attractors, it is possible to interpret these critical
points as tipping points. In other words, depending on the latent period, a
periodic attractor (predictability) can evolve to a chaotic attractor
(unpredictability). Therefore, we show that unpredictability is associated with
bistable dynamics preferably chaotic, and, furthermore, there is a tipping
point associated with unpredictable dynamics
Effects of drug resistance in the tumour-immune system with chemotherapy treatment
Acknowledgement This study was possible by partial financial support from the following Brazilian government agencies: Fundaao Araucaria, National Council for Scientific and Technological Development, Coordination for the Improvement of Higher Education Personnel, and Sao Paulo Research Foundation (2015/07311-7, 2017/18977- 1, 2018/03211-6, 2020/04624-2)Peer reviewedPostprin