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pro vyhledávání: '"39a28"'
In this work, we propose a generalization to the classical logistic map. The generalized map preserves most properties of the classical map and has richer dynamics as it contains the fractional order and one more parameter. We propose the stability b
Externí odkaz:
http://arxiv.org/abs/2409.07174
Autor:
Simpson, David J. W.
The border-collision normal form is a piecewise-linear family of continuous maps that describe the dynamics near border-collision bifurcations. Most prior studies assume each piece of the normal form is invertible, as is generic from an abstract view
Externí odkaz:
http://arxiv.org/abs/2408.04790
Autor:
Glendinning, P. A., Simpson, D. J. W.
The border-collision normal form describes the local dynamics in continuous systems with switches when a fixed point intersects a switching surface. For one-dimensional cases where the bifurcation creates or destroys only fixed points and period-two
Externí odkaz:
http://arxiv.org/abs/2407.16865
Publikováno v:
Journal of Difference Equations and Applications, 26(5), 643-656, 2020
Subthreshold oscillations in neurons are those oscillations which do not attain the critical value of the membrane's voltage needed for triggering an action potential (a spike). Their contribution to the forming of action potentials in neurons is a c
Externí odkaz:
http://arxiv.org/abs/2403.14219
Autor:
Simpson, David J. W.
Piecewise-smooth maps are used as discrete-time models of dynamical systems whose evolution is governed by different equations under different conditions (e.g.~switched control systems). By assigning a symbol to each region of phase space where the m
Externí odkaz:
http://arxiv.org/abs/2312.03887
Autor:
Simpson, D. J. W.
For piecewise-linear maps the stable and unstable manifolds of hyperbolic periodic solutions are themselves piecewise-linear. Hence compact subsets of these manifolds can be represented using polytopes (i.e. polygons, in the case of two-dimensional m
Externí odkaz:
http://arxiv.org/abs/2310.09941
This paper examines a discrete predator-prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator species. Furthermore, juvenile hunting as well as prey
Externí odkaz:
http://arxiv.org/abs/2308.08864
This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applications. The normal form was recently shown to exhibit a chaotic attrac
Externí odkaz:
http://arxiv.org/abs/2307.05144
Autor:
Glendinning, P. A., Simpson, D. J. W.
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity. We descri
Externí odkaz:
http://arxiv.org/abs/2303.00115
Autor:
Glendinning, P. A., Simpson, D. J. W.
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these phenomena
Externí odkaz:
http://arxiv.org/abs/2211.05917