Complex dynamics in a nerve fiber model with periodic coefficients

Zanini, Chiara; Zanolin, Fabio

doi:10.1016/j.nonrwa.2008.01.024

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…Similar examples of complex dynamics for the Poincaré map associated with differential systems have been discussed, e.g., in [61][62][63][64][65], using different methods. See also [1,31,66] for recent contributions in this direction. Now we are in position to state our main result for (17).…”

Section: Setting Of the Problem And Main Resultsmentioning

confidence: 99%

Complex Dynamics in One‐Dimensional Nonlinear Schrödinger Equations with Stepwise Potential

Zanini

Zanolin

2018

Complexity

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We prove the existence and multiplicity of periodic solutions as well as solutions presenting a complex behavior for the one-dimensional nonlinear Schrödinger equation -ε2u′′+V(x)u=f(u), where the potential V(x) approximates a two-step function. The term f(u) generalizes the typical p-power nonlinearity considered by several authors in this context. Our approach is based on some recent developments of the theory of topological horseshoes, in connection with a linked twist maps geometry, which are applied to the discrete dynamics of the Poincaré map. We discuss the periodic and the Neumann boundary conditions. The value of the term ε>0, although small, can be explicitly estimated.

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Section: Setting Of the Problem And Main Resultsmentioning

confidence: 99%

Complex Dynamics in One‐Dimensional Nonlinear Schrödinger Equations with Stepwise Potential

Zanini

Zanolin

2018

Complexity

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“…We also recall the related works[47,55], in which the existence of complex dynamics has been proved in a 2D and in a 3D continuous-time framework, respectively, by means of the SAP technique, without relying on the LTMs geometry.…”

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Chaotic dynamics in the presence of medical malpractice litigation: a topological proof via linked twist maps for two evolutionary game theoretic contexts

Pireddu¹

2020

Preprint

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In the present work we reconsider the evolutionary game theoretic models by Antoci et al. (2016Antoci et al. ( , 2018 describing the dynamic outcomes arising from the interactions between patients and physicians, whose behavior is subject to clinical and legal risks. In particular, Antoci et al. (2016) analyzed the case of positive defensive medicine, while Antoci et al. (2018) dealt with the case of negative defensive medicine. We show that, when the models admit a nonisochronous center, it is possible to prove the existence of chaotic dynamics for the Poincaré map associated with those systems via the method of Linked Twist Maps (LTMs). To such aim we exploit in both frameworks, using a similar rationale, the periodic dependence on time of a model parameter influencing the position of the center and describing some risk associated with certain medical interventions, whose seasonal variation is empirically grounded. We also provide the ecological interpretation of the same model, proposed by Harvie et al. (2007) and connected with intraspecific competition and environmental carrying capacity in predator-prey settings. In this case, it is sensible to assume a seasonal variation both for the carrying capacities and for the intrinsic growth rates of the two populations. Although such parameters influence the shape of the orbits, but do not affect the center position, we show that it is still possible to prove the existence of chaotic dynamics for the associated Poincaré map via the LTMs technique dealing with a different geometrical configuration for orbits in the phase plane.

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Chaos in predator–prey systems with/without impulsive effect

Ruiz-Herrera¹

2012

Nonlinear Analysis: Real World Applications

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Complex dynamics in a nerve fiber model with periodic coefficients

Cited by 4 publications

References 22 publications

Complex Dynamics in One‐Dimensional Nonlinear Schrödinger Equations with Stepwise Potential

Complex Dynamics in One‐Dimensional Nonlinear Schrödinger Equations with Stepwise Potential

Chaotic dynamics in the presence of medical malpractice litigation: a topological proof via linked twist maps for two evolutionary game theoretic contexts

Chaos in predator–prey systems with/without impulsive effect

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