Linear bifurcation analysis with applications to relative socio-spatial dynamics.
Sonis, M. (1997)
Discrete Dynamics in Nature and Society
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Sonis, M. (1997)
Discrete Dynamics in Nature and Society
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Discrete Dynamics in Nature and Society
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De Carvalho Braga, Denis, Mello, Luis Fernando, Messias, Marcelo (2009)
Mathematical Problems in Engineering
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Discrete Dynamics in Nature and Society
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Shu Dai, David G. Schaeffer (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either stationary or travelling, which is known as alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by Echebarria-Karma. As shown in our previous paper, the zero solution of their equation may...
Tramontana, Fabio, Gardini, Laura, Dieci, Roberto, Westerhoff, Frank (2009)
Discrete Dynamics in Nature and Society
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Discrete Dynamics in Nature and Society
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Mathematical Problems in Engineering
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Hongtao Liang, Yanxia Tang, Li Li, Zhouchao Wei, Zhen Wang (2013)
Kybernetika
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In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.