Capítols de llibre
http://hdl.handle.net/2117/90842
2024-03-29T14:55:06ZOn dynamics and invariant sets in predator-prey maps
http://hdl.handle.net/2117/174092
On dynamics and invariant sets in predator-prey maps
Lázaro Ochoa, José Tomás; Alsedà, Lluís; Sardañés, Josep; Vidiella, Blai
A multitude of physical, chemical, or biological systems evolving in discrete time can be modelled and studied using difference equations (or iterative maps). Here we discuss local and global dynamics for a predator-prey two-dimensional map. The system displays an enormous richness of dynamics including extinctions, co- extinctions, and both ordered and chaotic coexistence. Interestingly, for some regions we have found the so-called hyperchaos, here given by two positive
Lyapunov exponents. An important feature of biological dynamical systems, espe-cially in discrete time, is to know where the dynamics lives and asymptotically remains within the phase space, that is, which is the invariant set and how it evolves under parameter changes. We found that the invariant set for the predator-prey map is very sensitive to parameters, involving the presence of escaping regions for which the orbits go out of the domain of the system (the species overcome the
carrying capacity) and then go to extinction in a very fast manner. This theoretical finding suggests a potential dynamical fragility by which unexpected and sharp extinctions may take place.
2019-12-19T11:22:41ZLázaro Ochoa, José TomásAlsedà, LluísSardañés, JosepVidiella, BlaiA multitude of physical, chemical, or biological systems evolving in discrete time can be modelled and studied using difference equations (or iterative maps). Here we discuss local and global dynamics for a predator-prey two-dimensional map. The system displays an enormous richness of dynamics including extinctions, co- extinctions, and both ordered and chaotic coexistence. Interestingly, for some regions we have found the so-called hyperchaos, here given by two positive
Lyapunov exponents. An important feature of biological dynamical systems, espe-cially in discrete time, is to know where the dynamics lives and asymptotically remains within the phase space, that is, which is the invariant set and how it evolves under parameter changes. We found that the invariant set for the predator-prey map is very sensitive to parameters, involving the presence of escaping regions for which the orbits go out of the domain of the system (the species overcome the
carrying capacity) and then go to extinction in a very fast manner. This theoretical finding suggests a potential dynamical fragility by which unexpected and sharp extinctions may take place.How does the hopf bifurcation appear in the hydrogen atom in a Circularly Polarized (CP) microwave field?
http://hdl.handle.net/2117/174089
How does the hopf bifurcation appear in the hydrogen atom in a Circularly Polarized (CP) microwave field?
Ollé Torner, Mercè; Pacha Andújar, Juan Ramón
The dynamics of the Rydberg atom in a rotating electric field can be described by a two degree of freedom Hamiltoniandepending on a parameterK. This Hamiltonian has two equilibrium pointsL1andL2. WhileL1is a saddle-center for allvalues ofK, the hyperbolic character ofL2changes from a double center to a complex saddle as the parameterKcrossesa critical threshold, giving rise to the Hopf bifurcation. Here we analyze the dynamics close to this transition.
2019-12-19T11:17:14ZOllé Torner, MercèPacha Andújar, Juan RamónThe dynamics of the Rydberg atom in a rotating electric field can be described by a two degree of freedom Hamiltoniandepending on a parameterK. This Hamiltonian has two equilibrium pointsL1andL2. WhileL1is a saddle-center for allvalues ofK, the hyperbolic character ofL2changes from a double center to a complex saddle as the parameterKcrossesa critical threshold, giving rise to the Hopf bifurcation. Here we analyze the dynamics close to this transition.Computation of invariant curves in the analysis of periodically forced neural oscillators
http://hdl.handle.net/2117/127401
Computation of invariant curves in the analysis of periodically forced neural oscillators
Pérez Cervera, Alberto; Huguet Casades, Gemma; Martínez-Seara Alonso, M. Teresa
Background oscillations, reflecting the excitability of neurons, are ubiq- uitous in the brain. Some studies have conjectured that when spikes sent by one population reach the other population in the peaks of excitability, then informa- tion transmission between two oscillating neuronal groups is more effective. In this context, phase locking relationships between oscillating neuronal populations may have implications in neuronal communication as they assure synchronous activity between brain areas. To study this relationship, we consider a population rate model and perturb it with a time-dependent input. We use the stroboscopic map and apply powerful computational methods to compute the invariant objects and their bifur- cations as the perturbation parameters (frequency and amplitude) are varied. The analysis performed shows the relationship between the appearance of synchronous and asynchronous regimes and the invariant objects of the stroboscopic map.
2019-01-23T09:04:28ZPérez Cervera, AlbertoHuguet Casades, GemmaMartínez-Seara Alonso, M. TeresaBackground oscillations, reflecting the excitability of neurons, are ubiq- uitous in the brain. Some studies have conjectured that when spikes sent by one population reach the other population in the peaks of excitability, then informa- tion transmission between two oscillating neuronal groups is more effective. In this context, phase locking relationships between oscillating neuronal populations may have implications in neuronal communication as they assure synchronous activity between brain areas. To study this relationship, we consider a population rate model and perturb it with a time-dependent input. We use the stroboscopic map and apply powerful computational methods to compute the invariant objects and their bifur- cations as the perturbation parameters (frequency and amplitude) are varied. The analysis performed shows the relationship between the appearance of synchronous and asynchronous regimes and the invariant objects of the stroboscopic map.On bifurcations of homoclinic tangencies in area-preserving maps on non-orientable manifolds
http://hdl.handle.net/2117/101963
On bifurcations of homoclinic tangencies in area-preserving maps on non-orientable manifolds
Delshams Valdés, Amadeu; Gonchenko, Marina; Gonchenko, Sergey
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional manifolds. We consider one and two parameter general unfoldings and establish results related to the appearance of elliptic periodic orbits.
2017-03-06T11:00:45ZDelshams Valdés, AmadeuGonchenko, MarinaGonchenko, SergeyWe study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional manifolds. We consider one and two parameter general unfoldings and establish results related to the appearance of elliptic periodic orbits.Effects of thermoregulation on human sleep patterns: A mathematical model of sleep-wake cycles with REM-NREM subcircuit
http://hdl.handle.net/2117/90841
Effects of thermoregulation on human sleep patterns: A mathematical model of sleep-wake cycles with REM-NREM subcircuit
Bañuelos, Selenne; Best, Janet; Huguet Casades, Gemma; Prieto-Langarica, Alicia; Pyzza, Pamela; Schmidt, Markus; Wilson, Shelby
In this paper we construct a mathematical model of human sleep/wake regulation with thermoregulation and temperature e ects. Simulations of this model show features previously presented in experimental data such as elongation of duration and number of REM bouts across the night as well as the appearance of awakenings due to deviations in body temperature from thermoneutrality. This model helps to demonstrate the importance of temperature in the sleep cycle. Further modi cations of the model to include more temperature e ects on other aspects of sleep regulation such as sleep and REM latency are discussed
2016-10-18T10:52:04ZBañuelos, SelenneBest, JanetHuguet Casades, GemmaPrieto-Langarica, AliciaPyzza, PamelaSchmidt, MarkusWilson, ShelbyIn this paper we construct a mathematical model of human sleep/wake regulation with thermoregulation and temperature e ects. Simulations of this model show features previously presented in experimental data such as elongation of duration and number of REM bouts across the night as well as the appearance of awakenings due to deviations in body temperature from thermoneutrality. This model helps to demonstrate the importance of temperature in the sleep cycle. Further modi cations of the model to include more temperature e ects on other aspects of sleep regulation such as sleep and REM latency are discussed