Conservative generalized bifurcation diagrams and phase space properties for oval-like billiards

We propose a method for the design of electronic bursting neurons, based on a simple conductance neuron model. A burster is a particular class of neuron that displays fast spiking regimes alternating with resting periods. Our method is based on the use of an electronic circuit that implements the well-known Morris–Lecar neuron model. We use this circuit as a tool of analysis to explore some regions of the parameter space and to contruct several bifurcation diagrams displaying the basic dynamical features of that system. These bifurcation diagrams provide the initial point for the design and implementation of electronic bursting neurons. By extending the phase space with the introduction of a slow driving current, our method allows to exploit the bistabilities which are present in the Morris–Lecar system to the building of different bursting models.

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Spatial Dissipative Structures in Excitable Media (Plankton, Soil Bacteria. . . .)

Attractors and Higher Dimensions in Population and Molecular Biology - Advances in Bioinformatics and Biomedical Engineering ◽

10.4018/978-1-5225-9651-6.ch004 ◽

2019 ◽

pp. 91-126

Keyword(s):

Spatial Distribution ◽

Phase Space ◽

Dissipative Structure ◽

Dissipative Structures ◽

The Other ◽

Excitable Media ◽

Bifurcation Diagrams ◽

Dimensional Phase Space ◽

Liesegang Bands ◽

Space Characteristic

A general, the simplest model of a spatial dissipative structure arising in an excitable medium is constructed, containing at least two components interacting with each other with their own mobility. One of these components (active) uses the other component as food. It is shown that such a model leads to a stationary stable spatial distribution of the components in the form of Liesegang bands. As specific examples of the formation of spatial dissipative structures, structures arising in plankton consisting of phytoplankton and zooplankton and in the soil containing the bacterial population and the nutrient substrate are considered. Bifurcation diagrams are constructed in the parameter space, characteristic for each of the considered excitable media, which determine the conditions for the formation of dissipative structures in these media. The existence in the plankton of a strange attractor of a previously unknown shape in four-dimensional phase space has been discovered.

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Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator

Entropy ◽

10.3390/e21040384 ◽

2019 ◽

Vol 21 (4) ◽

pp. 384

Author(s):

Vicente Aboites ◽

David Liceaga ◽

Rider Jaimes-Reátegui ◽

Juan Hugo García-López

Keyword(s):

Phase Space ◽

Dynamic Behavior ◽

Periodic Orbits ◽

Ring Resonator ◽

Matrix Elements ◽

Bifurcation Diagrams ◽

Direct Dependence ◽

Computer Calculations ◽

Generating Matrix ◽

Explicit Expressions

In this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements were obtained. Furthermore, computer calculations for several parameter configurations were made; rich dynamic behavior among periodic orbits high periodicity and chaos were observed through bifurcation diagrams. These results confirm the direct dependence between the parameters present in the intracavity chaos-generating element.

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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