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One question raised by these studies is whether Lotka-Volterra type dynamics is necessary to give robust heteroclinic cycles as attractors and how these cycles relate to those found in other models [9, 10].
The modified propofol model is given as a six-dimensional conductance based model with Hodgkin–Huxley type dynamics: c m d V d t = − I Na − I K − I L − I M − I syn + I app, d x d t = ( x ∞ ( V ) − x ) τ x ( V ), x = m, h, n, w, d s d t = − s / τ s, (1).
Whereas the considered neural network model may be perceived to some extent simplistic, its asymptotic description in terms of a winner-take-all type dynamics and hence also the scale-free nature of the spike flow graph seem to be rather universal as suggested both by a theoretical argument and by numerical evidence for various neuronal models.
We argue that for independent Gaussian weights in low enough temperature the large-scale behavior of the system admits an accurate description in terms of a winner-take-all type dynamics which can be used for showing that the resulting graph of charge transfers, referred to as the spike flow graph in the sequel, has scale-free properties with power law exponent γ= 2.
The plasma evaporation from chromospheric and transition region heights eventually causes localised runaway condensation events and we witness the formation of plasma blobs due to thermal instability, that evolve dynamically in the heated arcade part and move gradually downwards due to interchange type dynamics.
We apply now the spring-block system and a relaxation type dynamics for detecting regions on different length-scales.
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New estimates for Glauber-type dynamics are also obtained.
An application to the Glauber-type dynamics with competitions is considered.
The objective of this section is to perform a qualitative analysis of system (1.6) and derive the Allee-type dynamics.
As a result, the canopy gradually opens up and a cohort-type dynamics and tree age distribution and emerge.
Similar results are derived for Kawasaki-type dynamics in the lattice without exclusion, and in the continuum.
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