arXiv subjects

Jesús M. Seoane

Publications and source records attributed to Jesús M. Seoane.

26 records · Page 2Linked to original sources

arXiv2019

Measuring the transition between nonhyperbolic and hyperbolic regimes in open Hamiltonian systems

We show that the presence of KAM islands in nonhyperbolic chaotic scattering has deep implications on the unpredictability of open Hamiltonian systems. When the energy of the system increases the particles escape faster. For this reason the boundary of the exit basins becomes thinner and less fractal. Hence, we could expect a monotonous decrease in the unpredictability as well as in the fractal dimension. However, within the nonhyperbolic regime, fluctuations in the basin entropy have been uncovered. The reason is that when increasing the energy, both the size and geometry of the KAM islands undergo abrupt changes. These fluctuations do not appear within the hyperbolic regime. Hence, the fluctuations in the basin entropy allow us to ascertain the hyperbolic or nonhyperbolic nature of a system. In this manuscript we have used continuous and discrete open Hamiltonian systems in order to show the relevant role of the KAM islands on the unpredictability, and the utility of the basin entropy to analyze this kind of systems.

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arXiv2019

Delay-Induced Resonance in the Time-Delayed Duffing Oscillator

The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the parameters for which the time-delay induces sustained oscillations. Here, we study this type of resonance in the overdamped and underdamped time-delayed Duffing oscillators, and we explore some new features. One of them is the conjugate phenomenon: the oscillations caused by the time-delay may be enhanced by means of the forcing without modifying their frequency. The resonance takes place when the frequency of the oscillations induced by the time-delay matches the ones caused by the forcing and vice versa. This is an interesting result as the nature of both perturbations is different. Even for the parameters for which the time-delay does not induce sustained oscillations, we show that a resonance may appear following a different mechanism.

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arXiv2019

The role of dose-density in combination cancer chemotherapy

A multicompartment mathematical model is presented with the goal of studying the role of dose-dense protocols in the context of combination cancer chemotherapy. Dose-dense protocols aim at reducing the period between courses of chemotherapy from three to two weeks or less, in order to avoid the regrowth of the tumor during the meantime and achieve maximum cell kill at the end of the treatment. Inspired by clinical trials, we carry out a randomized computational study to systematically compare a variety of protocols using two drugs of different specificity. Our results suggest that cycle specific drugs can be administered at low doses between courses of treatment to arrest the relapse of the tumor. This might be a better strategy than reducing the period between cycles.

q-bio.PE↗

arXiv2018

Computing complex horseshoes by means of piecewise maps

A systematic procedure to numerically compute a horseshoe map is presented. This new method uses piecewise functions and expresses the required operations by means of elementary transformations, such as translations, scalings, projections and rotations. By repeatedly combining such transformations, arbitrarily complex folding structures can be created. We show the potential of these horseshoe piecewise maps to illustrate several central concepts of nonlinear dynamical systems, as for example the Wada property.

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arXiv2018

Nonlinear cancer chemotherapy: modelling the Norton-Simon hypothesis

A fundamental model of tumor growth in the presence of cytotoxic chemotherapeutic agents is formulated. The model allows to study the role of the Norton-Simon hypothesis in the context of dose-dense chemotherapy. Dose-dense protocols aim at reducing the period between courses of chemotherapy from three weeks to two weeks, in order to avoid tumor regrowth between cycles. We address the conditions under which these protocols might be more or less beneficial in comparison to less dense settings, depending on the sensitivity of the tumor cells to the cytotoxic drugs. The effects of varying other parameters of the protocol, as for example the duration of each continuous drug infusion, are also inspected. We believe that the present model might serve as a foundation for the development of more sophisticated models for cancer chemotherapy.

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arXiv2018

Resonant behavior and unpredictability in forced chaotic scattering

Chaotic scattering in open Hamiltonian systems is a topic of fundamental interest in physics, which has been mainly studied in the purely conservative case. However, the effect of weak perturbations in this kind of systems has been an important focus of interest in the last decade. In a previous work, the authors studied the effects of a periodic forcing in the decay law of the survival probability, and they characterized the global properties of escape dynamics. In the present paper, we add two important issues in the effects of periodic forcing: the fractal dimension of the set of singularities in the scattering function, and the unpredictability of the exit basins, which is estimated by using the concept of basin entropy. Both the fractal dimension and the basin entropy exhibit a resonant-like decrease as the forcing frequency increases. We provide a theoretical reasoning, which could justify this decreasing in the fractality near the main resonant frequency, that appears for $ω\approx 1$. We attribute the decrease in the basin entropy to the reduction of the area occupied by the KAM islands and the basin boundaries when the frequency is close to the resonance. Finally, the decay rate of the exponential decay law shows a minimum value of the amplitude, $A_c$, which reflects the complete destruction of the KAM islands in the resonance. We expect that this work could be potentially useful in research fields related to chaotic Hamiltonian pumps, oscillations in chemical reactions and companion galaxies, among others.

nlin.CD↗

arXiv2018

Uncertainty dimension and basin entropy in relativistic chaotic scattering

Chaotic scattering is an important topic in nonlinear dynamics and chaos with applications in several fields in physics and engineering. The study of this phenomenon in relativistic systems has receivedlittle attention as compared to the Newtonian case. Here, we focus our work on the study of some relevant characteristics of the exit basin topology in the relativistic Hénon-Heiles system: the uncertainty dimension, the Wada property and the basin entropy. Our main findings for the uncertainty dimension show two different behaviors insofar we change the relativistic parameter $β$, in which a crossover behavior is uncovered. This crossover point is related with the disappearance of KAM islands in phase space that happens for velocity values above the ultra-relativistic limit, $v>0.1c$. This result is supported by numerical simulations and also by qualitative analysis, which are in good agreement. On the other hand, the computation of the exit basins in the phase space suggests the existence of Wada basins for a range of $β<0.625$. We also studied the evolution of the exit basins in a quantitative manner by computing the basin entropy, which shows a maximum value for $β\approx 0.2$. This last quantity is related to the uncertainty in the prediction of the final fate of the system. Finally, our work is relevant in galactic dynamics and it also has important implications in other topics in physics as in the Störmer problem, among others.

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arXiv2016

On the fractional cell kill law governing the lysis of solid tumors

We present in silico simulations and mathematical analyses supporting several hypotheses that explain the saturation expressed in the fractional cell kill law that governs the lysis of tumor cells by cytotoxic CD8 + T cells (CTLs). In order to give insight into the significance of the parameters appearing in such law, a hybrid cellular automaton model describing the spatio-temporal evolution of tumor growth and its interaction with the cell-mediated immune response is used. When the CTLs eradicate efficiently the tumor cells, the model predicts a correlation between the morphology of the tumors and the rate at which they are lysed. As the effectiveness of the effector cells is decreased, the saturation gradually disappears. This limit is thoroughly discussed and a new fractional cell kill is proposed.

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