Felix Borotto - Academia.edu (original) (raw)

Papers by Felix Borotto

Reviews of Modern Plasma Physics

Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astr... more Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review the theory of deterministic and stochastic temporal chaos in plasmas and discuss its link to intermittent turbulence observed in space plasmas. First, we discuss the theory of chaos, intermittency, and complexity for nonlinear Alfvén waves, and parametric decay and modulational wave–wave interactions, in the absence/presence of noise. The transition from order to chaos is studied using the bifurcation diagram. The following two types of deterministic intermittent chaos in plasmas are considered: type-I Pomeau–Manneville intermittency and crisis-induced intermittency. The role of structures known as chaotic saddles in deterministic and stochastic chaos in plasmas is investigated. Alfvén complexity associated with noise-induced intermittency, in the presence of multistability, is studied. Next, we present evidence of magnetic reconnection and in...

Physical review, May 5, 2022

Epstein's model for a civil disorder is an agent-based model that simulates a social protest proc... more Epstein's model for a civil disorder is an agent-based model that simulates a social protest process where the central authority uses the police force to dissuade it. The interactions of police officers and citizens produce dynamics that do not yet have any analysis from the sociophysics approach. We present numerical simulations to characterize the properties of the one-dimensional civil disorder model on stationary-state. To do this, we consider interactions on a Moore neighborhood and a random neighborhood with two different visions. We introduce a Potts-like energy function and construct the phase diagram using the agent state concentration. We find order-disorder phases and reveal the principle of minimum grievance as the underlying principle of the model's dynamics. Besides, we identify when the system can reach stable or an instability conditions based on the agents' interactions. Finally, we identified the most relevant role of the police based on their capacity to dissuade a protest and their effect on facilitating a stable scenario.

Research Papers in Economics, 2018

It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribu... more It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of Gamma distributions corresponding to particular subsets of agents. Here, we propose a new four-parameter statistical distribution which is a kappa\kappakappa-deformation of the Generalized Gamma distribution with a power-law tail, based on the deformed exponential and logarithm functions introduced by Kaniadakis(2001). We found that this new distribution is also an extension to the kappa\kappakappa-Generalized distribution proposed by Clementi et al. (2007), with an additional shape parameter nu\nunu, and properly reproduces the whole range of the distribution of wealth in such heterogeneous kinetic exchange models. We also provide various associated statistical measures and inequality measures.

The civil violence model is agent-based simulates a social protest process where the police force... more The civil violence model is agent-based simulates a social protest process where the police force restores public order. The interactions of cops and citizens produce dynamics that do not yet have any analysis from the sociophysics approach. We present numerical simulations to characterize the properties of the one-dimensional civil violence model on stationary-state. To do this, we consider shortand long-range interactions on a Moore neighborhood and a random neighborhood, a Pottslike energy function, and construct the phase diagram. We find order-disorder phases like those observed in the opinion models. These results are a first approach to studying this model in other dimensions and topologies and considering other complexities of social protest dynamics.

Physica A: Statistical Mechanics and its Applications, 2021

Physica A: Statistical Mechanics and its Applications, 2019

It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribu... more It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of Gamma distributions corresponding to particular subsets of agents. Here, we propose a new fourparameter statistical distribution which is a κ-deformation of the Generalized Gamma distribution with a power-law tail, based on the deformed exponential and logarithm functions introduced by Kaniadakis(2001). We found that this new distribution is also an extension to the κ-Generalized distribution proposed by Clementi et al. (2007), with an additional shape parameter ν, and properly reproduces the whole range of the distribution of wealth in such heterogeneous kinetic exchange models. We also provide various associated statistical measures and inequality measures.

Advances in Space Environment Research - Volume I, 2003

Space plasmas are dominated by waves, instabilities and turbulence. Dynamical systems approach of... more Space plasmas are dominated by waves, instabilities and turbulence. Dynamical systems approach offers powerful mathematical and computational techniques to probe the origin and nature of space environment turbulence. Using the nonlinear dynamics tools such as the bifurcation diagram and Poincaré maps, we study the transition from order to chaos, from weak to strong chaos, and the destruction of a chaotic attractor. The characterization of the complex system dynamics of the space environment, such as the Alfvén turbulence, can improve the capability of monitoring Sun-Earth connections and prediction of space weather.

Planetary and Space Science, 2000

ABSTRACT A dynamical theory of nonlinear three-wave interactions involving Langmuir, whistler and... more ABSTRACT A dynamical theory of nonlinear three-wave interactions involving Langmuir, whistler and Alfvén waves in the planetary magnetospheres is developed. By assuming linear growth for the Langmuir wave and linear damping for both whistler and Alfvén waves, the wave triplet is shown to evolve temporarily from order to chaos via either the period doubling route or the type-I Pomeau–Manneville intermittency route. Numerical solutions of this dynamical system are presented, showing the time series of the wave amplitude and the corresponding power spectra. The characterization of orderly and chaotic states is performed by plotting the Poincaré maps and calculating the largest Lyapunov exponent. The relevance of this theory for observation of chaos in the time series of nonthermal planetary radio emissions is discussed.

Physica A: Statistical Mechanics and its Applications, 2000

The possibility of nonlinear interaction between Langmuir waves and ion-acoustic waves in the sol... more The possibility of nonlinear interaction between Langmuir waves and ion-acoustic waves in the solar wind has received considerable interest in the last years. However, little attention has been paid to the possibility of nonlinear coupling between Langmuir waves and whistler waves in the interplanetary medium. Close temporal correlation between high-frequency Langmuir waves and low-frequency electromagnetic whistler waves has been observed recently within magnetic holes of the solar wind. In order to account for these observations within magnetic holes of the solar wind, we develop a nonlinear three-wave theory describing the parametric interaction of Langmuir waves, electromagnetic whistler waves with either right-or left-hand circularly polarized electromagnetic waves. We suggest that the nonlinear coupling of Langmuir waves and whistler waves may lead to the formation of modulated Langmuir wave packets as well as the generation of circularly polarized radio waves at the plasma frequency in the solar wind.

Advances in Space Research, 2001

Narrowband spiky radio bursts, at decimetric and decametric wavelengths, with high degree of circ... more Narrowband spiky radio bursts, at decimetric and decametric wavelengths, with high degree of circular polarization are observed in solar flares. We discuss a new plasma emission mechanism for solar radio spikes. It is shown that narrowband radio bursts of right-and left-hand circular polarizations can be produced via nonlinear conversion of Langmuir waves into high-frequency electromagnetic electron cyclotron waves near the plasma frequency by coupling to low-frequency electromagnetic cyclotron waves such as Alfven-ion cyclotron or magnetosonic-whistler waves.

Nonlinear Processes in Geophysics, 2007

The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schröd... more The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddlenode bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gapfilling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

8th International Congress of the Brazilian Geophysical Society

Symposium - International Astronomical Union

Electron cyclotron maser emission is an accepted physical mechanism for generating coherent plane... more Electron cyclotron maser emission is an accepted physical mechanism for generating coherent planetary and stellar radio emissions. Observational data has indicated evidence of nonlinear and chaotic temporal variability in some cosmic masers such as solar microwave spikes. The nonlinear and chaotic characteristics of cosmic masers can be attributed to plasma turbulence, such as Alfvén chaos, embedded in the emission region. We report a chaos theory of Alfvén waves which can account for chaotic acceleration of electrons in the source region of cosmic masers. Two types of Alfvén intermittency are identified: Pomeau-Manneville intermittency and crisis-induced intermittency. Since Alfvén waves may be responsible for accelerating electrons that emit maser radiations, the chaotic dynamics of Alfvén waves may be the origin of chaotic time variations of cosmic masers. Hence, we suggest that Alfvén intermittency may cause intermittent temporal fluctuations which can be observed in cosmic masers.

Scientific reports, Jan 12, 2018

Equatorial plasma depletions have significant impact on radio wave propagation in the upper atmos... more Equatorial plasma depletions have significant impact on radio wave propagation in the upper atmosphere, causing rapid fluctuations in the power of radio signals used in telecommunication and GPS navigation, thus playing a crucial role in space weather impacts. Complex structuring and self-organization of equatorial plasma depletions involving bifurcation, connection, disconnection and reconnection are the signatures of nonlinear evolution of interchange instability and secondary instabilities, responsible for the generation of coherent structures and turbulence in the ionosphere. The aims of this paper are three-fold: (1) to report the first optical imaging of reconnection of equatorial plasma depletions in the South Atlantic Magnetic Anomaly, (2) to investigate the optical imaging of equatorial ionospheric intermittent turbulence, and (3) to compare nonlinear characteristics of optical imaging of equatorial plasma depletions for two different altitudes at same times. We show that t...

Physica D Nonlinear Phenomena, Jul 1, 2004

Chaotic transitions of nonlinear Alfvén waves via boundary and interior crises are studied. Alfvé... more Chaotic transitions of nonlinear Alfvén waves via boundary and interior crises are studied. Alfvén crises are characterized using the unstable periodic orbits and their stable and unstable manifolds. In a period-3 periodic window of the bifurcation diagram, we identify a period-9 unstable periodic orbit that is responsible for both boundary and interior crises of two chaotic attractors. We demonstrate that these Alfvén crises arise from a homoclinic tangency.

Space Science Reviews, 2003

Nonthermal magnetospheric radio emissions provide the radio signatures of solar-terrestrial conne... more Nonthermal magnetospheric radio emissions provide the radio signatures of solar-terrestrial connection and may be used for space weather forecasting. A three-wave model of auroral radio emissions at the fundamental plasma frequency was proposed by Chian et al. (1994) involving resonant interactions of Langmuir, whistler and Alfvén waves. Chaos can appear in the nonlinear evolution of this three-wave process in the magnetosphere. We discuss two types of intermittency in radio signals driven by temporal chaos: the type-I Pomeau-Manneville intermittency and the interior crisis-induced intermittency. Examples of time series for both types of intermittency are presented.

Nonlinear Process Geophys, 2007

AIP Conference Proceedings, 2003

ABSTRACT Alfvén waves are important for heating and particle acceleration in space, astrophysical... more ABSTRACT Alfvén waves are important for heating and particle acceleration in space, astrophysical and laboratory plasmas. Chaos and intermittent turbulence of Alfvén waves have been observed in the solar wind. We show that the onset/destruction of Alfvén chaos can occur via a transition mechanism known as boundary crisis. A crisis is a global bifurcation whereby a chaotic (strange) attractor abruptly expands in size or vanishes along with its basin of attraction. Recent theoretical and experimental studies have confirmed that interior and boundary crises can occur in plasmas. We identify a boundary crisis in a complex plasma region in the presence of a large number of coexisting attractors. An example of double boundary crises is characterised using the unstable periodic orbit determined numerically from the numerical solution of the driven-dissipative nonlinear Schrödinger equation, which describes the nonlinear dynamics of a large-amplitude, left-hand circularly polarised Alfvén wave propagating along an ambient magnetic field. We demonstrate how the same unstable periodic orbit causes the appearance/disappearance of two chaotic attractors due to two successive homoclinic tangencies. The theoretical tools developed in this paper can be applied to detect Alfvén crises and other nonlinear dynamical Alfvénic phenomena in laboratory experiments as well as in space observations of interplanetary Alfvén turbulence.

Reviews of Modern Plasma Physics

Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astr... more Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review the theory of deterministic and stochastic temporal chaos in plasmas and discuss its link to intermittent turbulence observed in space plasmas. First, we discuss the theory of chaos, intermittency, and complexity for nonlinear Alfvén waves, and parametric decay and modulational wave–wave interactions, in the absence/presence of noise. The transition from order to chaos is studied using the bifurcation diagram. The following two types of deterministic intermittent chaos in plasmas are considered: type-I Pomeau–Manneville intermittency and crisis-induced intermittency. The role of structures known as chaotic saddles in deterministic and stochastic chaos in plasmas is investigated. Alfvén complexity associated with noise-induced intermittency, in the presence of multistability, is studied. Next, we present evidence of magnetic reconnection and in...

Physical review, May 5, 2022

Epstein's model for a civil disorder is an agent-based model that simulates a social protest proc... more Epstein's model for a civil disorder is an agent-based model that simulates a social protest process where the central authority uses the police force to dissuade it. The interactions of police officers and citizens produce dynamics that do not yet have any analysis from the sociophysics approach. We present numerical simulations to characterize the properties of the one-dimensional civil disorder model on stationary-state. To do this, we consider interactions on a Moore neighborhood and a random neighborhood with two different visions. We introduce a Potts-like energy function and construct the phase diagram using the agent state concentration. We find order-disorder phases and reveal the principle of minimum grievance as the underlying principle of the model's dynamics. Besides, we identify when the system can reach stable or an instability conditions based on the agents' interactions. Finally, we identified the most relevant role of the police based on their capacity to dissuade a protest and their effect on facilitating a stable scenario.

Research Papers in Economics, 2018

It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribu... more It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of Gamma distributions corresponding to particular subsets of agents. Here, we propose a new four-parameter statistical distribution which is a kappa\kappakappa-deformation of the Generalized Gamma distribution with a power-law tail, based on the deformed exponential and logarithm functions introduced by Kaniadakis(2001). We found that this new distribution is also an extension to the kappa\kappakappa-Generalized distribution proposed by Clementi et al. (2007), with an additional shape parameter nu\nunu, and properly reproduces the whole range of the distribution of wealth in such heterogeneous kinetic exchange models. We also provide various associated statistical measures and inequality measures.

The civil violence model is agent-based simulates a social protest process where the police force... more The civil violence model is agent-based simulates a social protest process where the police force restores public order. The interactions of cops and citizens produce dynamics that do not yet have any analysis from the sociophysics approach. We present numerical simulations to characterize the properties of the one-dimensional civil violence model on stationary-state. To do this, we consider shortand long-range interactions on a Moore neighborhood and a random neighborhood, a Pottslike energy function, and construct the phase diagram. We find order-disorder phases like those observed in the opinion models. These results are a first approach to studying this model in other dimensions and topologies and considering other complexities of social protest dynamics.

Physica A: Statistical Mechanics and its Applications, 2021

Physica A: Statistical Mechanics and its Applications, 2019

It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribu... more It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of Gamma distributions corresponding to particular subsets of agents. Here, we propose a new fourparameter statistical distribution which is a κ-deformation of the Generalized Gamma distribution with a power-law tail, based on the deformed exponential and logarithm functions introduced by Kaniadakis(2001). We found that this new distribution is also an extension to the κ-Generalized distribution proposed by Clementi et al. (2007), with an additional shape parameter ν, and properly reproduces the whole range of the distribution of wealth in such heterogeneous kinetic exchange models. We also provide various associated statistical measures and inequality measures.

Advances in Space Environment Research - Volume I, 2003

Space plasmas are dominated by waves, instabilities and turbulence. Dynamical systems approach of... more Space plasmas are dominated by waves, instabilities and turbulence. Dynamical systems approach offers powerful mathematical and computational techniques to probe the origin and nature of space environment turbulence. Using the nonlinear dynamics tools such as the bifurcation diagram and Poincaré maps, we study the transition from order to chaos, from weak to strong chaos, and the destruction of a chaotic attractor. The characterization of the complex system dynamics of the space environment, such as the Alfvén turbulence, can improve the capability of monitoring Sun-Earth connections and prediction of space weather.

Planetary and Space Science, 2000

ABSTRACT A dynamical theory of nonlinear three-wave interactions involving Langmuir, whistler and... more ABSTRACT A dynamical theory of nonlinear three-wave interactions involving Langmuir, whistler and Alfvén waves in the planetary magnetospheres is developed. By assuming linear growth for the Langmuir wave and linear damping for both whistler and Alfvén waves, the wave triplet is shown to evolve temporarily from order to chaos via either the period doubling route or the type-I Pomeau–Manneville intermittency route. Numerical solutions of this dynamical system are presented, showing the time series of the wave amplitude and the corresponding power spectra. The characterization of orderly and chaotic states is performed by plotting the Poincaré maps and calculating the largest Lyapunov exponent. The relevance of this theory for observation of chaos in the time series of nonthermal planetary radio emissions is discussed.

Physica A: Statistical Mechanics and its Applications, 2000

The possibility of nonlinear interaction between Langmuir waves and ion-acoustic waves in the sol... more The possibility of nonlinear interaction between Langmuir waves and ion-acoustic waves in the solar wind has received considerable interest in the last years. However, little attention has been paid to the possibility of nonlinear coupling between Langmuir waves and whistler waves in the interplanetary medium. Close temporal correlation between high-frequency Langmuir waves and low-frequency electromagnetic whistler waves has been observed recently within magnetic holes of the solar wind. In order to account for these observations within magnetic holes of the solar wind, we develop a nonlinear three-wave theory describing the parametric interaction of Langmuir waves, electromagnetic whistler waves with either right-or left-hand circularly polarized electromagnetic waves. We suggest that the nonlinear coupling of Langmuir waves and whistler waves may lead to the formation of modulated Langmuir wave packets as well as the generation of circularly polarized radio waves at the plasma frequency in the solar wind.

Advances in Space Research, 2001

Narrowband spiky radio bursts, at decimetric and decametric wavelengths, with high degree of circ... more Narrowband spiky radio bursts, at decimetric and decametric wavelengths, with high degree of circular polarization are observed in solar flares. We discuss a new plasma emission mechanism for solar radio spikes. It is shown that narrowband radio bursts of right-and left-hand circular polarizations can be produced via nonlinear conversion of Langmuir waves into high-frequency electromagnetic electron cyclotron waves near the plasma frequency by coupling to low-frequency electromagnetic cyclotron waves such as Alfven-ion cyclotron or magnetosonic-whistler waves.

Nonlinear Processes in Geophysics, 2007

The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schröd... more The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddlenode bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gapfilling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

8th International Congress of the Brazilian Geophysical Society

Symposium - International Astronomical Union

Electron cyclotron maser emission is an accepted physical mechanism for generating coherent plane... more Electron cyclotron maser emission is an accepted physical mechanism for generating coherent planetary and stellar radio emissions. Observational data has indicated evidence of nonlinear and chaotic temporal variability in some cosmic masers such as solar microwave spikes. The nonlinear and chaotic characteristics of cosmic masers can be attributed to plasma turbulence, such as Alfvén chaos, embedded in the emission region. We report a chaos theory of Alfvén waves which can account for chaotic acceleration of electrons in the source region of cosmic masers. Two types of Alfvén intermittency are identified: Pomeau-Manneville intermittency and crisis-induced intermittency. Since Alfvén waves may be responsible for accelerating electrons that emit maser radiations, the chaotic dynamics of Alfvén waves may be the origin of chaotic time variations of cosmic masers. Hence, we suggest that Alfvén intermittency may cause intermittent temporal fluctuations which can be observed in cosmic masers.

Scientific reports, Jan 12, 2018

Equatorial plasma depletions have significant impact on radio wave propagation in the upper atmos... more Equatorial plasma depletions have significant impact on radio wave propagation in the upper atmosphere, causing rapid fluctuations in the power of radio signals used in telecommunication and GPS navigation, thus playing a crucial role in space weather impacts. Complex structuring and self-organization of equatorial plasma depletions involving bifurcation, connection, disconnection and reconnection are the signatures of nonlinear evolution of interchange instability and secondary instabilities, responsible for the generation of coherent structures and turbulence in the ionosphere. The aims of this paper are three-fold: (1) to report the first optical imaging of reconnection of equatorial plasma depletions in the South Atlantic Magnetic Anomaly, (2) to investigate the optical imaging of equatorial ionospheric intermittent turbulence, and (3) to compare nonlinear characteristics of optical imaging of equatorial plasma depletions for two different altitudes at same times. We show that t...

Physica D Nonlinear Phenomena, Jul 1, 2004

Chaotic transitions of nonlinear Alfvén waves via boundary and interior crises are studied. Alfvé... more Chaotic transitions of nonlinear Alfvén waves via boundary and interior crises are studied. Alfvén crises are characterized using the unstable periodic orbits and their stable and unstable manifolds. In a period-3 periodic window of the bifurcation diagram, we identify a period-9 unstable periodic orbit that is responsible for both boundary and interior crises of two chaotic attractors. We demonstrate that these Alfvén crises arise from a homoclinic tangency.

Space Science Reviews, 2003

Nonthermal magnetospheric radio emissions provide the radio signatures of solar-terrestrial conne... more Nonthermal magnetospheric radio emissions provide the radio signatures of solar-terrestrial connection and may be used for space weather forecasting. A three-wave model of auroral radio emissions at the fundamental plasma frequency was proposed by Chian et al. (1994) involving resonant interactions of Langmuir, whistler and Alfvén waves. Chaos can appear in the nonlinear evolution of this three-wave process in the magnetosphere. We discuss two types of intermittency in radio signals driven by temporal chaos: the type-I Pomeau-Manneville intermittency and the interior crisis-induced intermittency. Examples of time series for both types of intermittency are presented.

Nonlinear Process Geophys, 2007

AIP Conference Proceedings, 2003

ABSTRACT Alfvén waves are important for heating and particle acceleration in space, astrophysical... more ABSTRACT Alfvén waves are important for heating and particle acceleration in space, astrophysical and laboratory plasmas. Chaos and intermittent turbulence of Alfvén waves have been observed in the solar wind. We show that the onset/destruction of Alfvén chaos can occur via a transition mechanism known as boundary crisis. A crisis is a global bifurcation whereby a chaotic (strange) attractor abruptly expands in size or vanishes along with its basin of attraction. Recent theoretical and experimental studies have confirmed that interior and boundary crises can occur in plasmas. We identify a boundary crisis in a complex plasma region in the presence of a large number of coexisting attractors. An example of double boundary crises is characterised using the unstable periodic orbit determined numerically from the numerical solution of the driven-dissipative nonlinear Schrödinger equation, which describes the nonlinear dynamics of a large-amplitude, left-hand circularly polarised Alfvén wave propagating along an ambient magnetic field. We demonstrate how the same unstable periodic orbit causes the appearance/disappearance of two chaotic attractors due to two successive homoclinic tangencies. The theoretical tools developed in this paper can be applied to detect Alfvén crises and other nonlinear dynamical Alfvénic phenomena in laboratory experiments as well as in space observations of interplanetary Alfvén turbulence.