Hicks' trade cycle revisited: cycles and bifurcations
In the Trade Cycle, Hicks introduced the idea that endogenous fluctuations could be coupled
with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a …
with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a …
On period-adding sequences of attracting cycles in piecewise linear maps
YL Maistrenko, VL Maistrenko, SI Vikul - Chaos, Solitons & Fractals, 1998 - Elsevier
We study numerically bifurcations in a family of bimodal three-piecewise linear continuous
one-dimensional maps. Attention is paid to the attracting cycles arising after the bifurcation …
one-dimensional maps. Attention is paid to the attracting cycles arising after the bifurcation …
Border-collision period-doubling scenario
V Avrutin, M Schanz - Physical Review E—Statistical, Nonlinear, and Soft …, 2004 - APS
Using a one-dimensional dynamical system, representing a Poincaré return map for
dynamical systems of the Lorenz type, we investigate the border-collision period-doubling …
dynamical systems of the Lorenz type, we investigate the border-collision period-doubling …
Period-doubling scenario without flip bifurcations in a one-dimensional map
V Avrutin, M Schanz - International Journal of Bifurcation and Chaos, 2005 - World Scientific
In this work a one-dimensional piecewise-smooth dynamical system, representing a
Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system …
Poincaré return map for dynamical systems of the Lorenz type, is investigated. The system …
The bandcount increment scenario. III. Deformed structures
V Avrutin, B Eckstein, M Schanz - Proceedings of the …, 2009 - royalsocietypublishing.org
Bifurcation structures in two-dimensional parameter spaces formed by chaotic attractors
alone are still a long way from being understood completely. In a series of three papers, we …
alone are still a long way from being understood completely. In a series of three papers, we …
Coexistence of the Bandcount‐Adding and Bandcount‐Increment Scenarios
V Avrutin, M Schanz, B Schenke - Discrete Dynamics in Nature …, 2011 - Wiley Online Library
We investigate the structure of the chaotic domain of a specific one‐dimensional piecewise
linear map with one discontinuity. In this system, the region of “robust" chaos is embedded …
linear map with one discontinuity. In this system, the region of “robust" chaos is embedded …
Ideal turbulence and problems of its visualization
AN Sharkovsky - Difference Equations, Special Functions And …, 2007 - World Scientific
Ideal turbulence is a mathematical phenomenon which occurs in certain infinite-dimensional
deterministic dynamical systems and implies that the attractor of a system lies off the phase …
deterministic dynamical systems and implies that the attractor of a system lies off the phase …
Systems of coupled piecewise-linear maps with central element: Stability of a synchronized state
IV Omel'chenko - Nonlinear Oscillations, 2005 - Springer
We investigate the stability of a synchronized state in systems of coupled one-dimensional
piecewise-linear maps that, by construction, contain a central element, ie, an element that …
piecewise-linear maps that, by construction, contain a central element, ie, an element that …
Stability of synchronized and clustered states in a system of coupled piecewise-linear maps
IV Matskiv - Nonlinear Oscillations, 2004 - Springer
Parameter regions for different types of stability of synchronized and clustered states are
obtained for two interacting ensembles of globally coupled one-dimensional piecewise …
obtained for two interacting ensembles of globally coupled one-dimensional piecewise …