States and transitions in mixed networks

A network is named as mixed network if it is composed of N nodes, the dynamics of some nodes are periodic, while the others are chaotic. The mixed network with all-to-all coupling and its corresponding networks after the nonlinearity gap-condition pruning are investigated. Several synchronization states are demonstrated in both systems, and a first-order phase transition is proposed. The mixture of dynamics implies any kind of synchronous dynamics for the whole network, and the mixed networks may be controlled by the nonlinearity gap-condition pruning.

[1]  Enrique Peacock-López,et al.  Switching induced complex dynamics in an extended logistic map , 2012 .

[2]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[3]  D. Papo,et al.  Explosive transitions to synchronization in networks of phase oscillators , 2012, Scientific Reports.

[4]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[5]  J. Spencer,et al.  Explosive Percolation in Random Networks , 2009, Science.

[6]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[7]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[8]  D. Kleinfeld,et al.  Traveling Electrical Waves in Cortex Insights from Phase Dynamics and Speculation on a Computational Role , 2001, Neuron.

[9]  B. Kahng,et al.  Percolation transitions in scale-free networks under the Achlioptas process. , 2009, Physical review letters.

[10]  J. Almeida,et al.  Can two chaotic systems give rise to order , 2004, nlin/0406010.

[11]  Michael Small,et al.  Basin of attraction determines hysteresis in explosive synchronization. , 2014, Physical review letters.

[12]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[13]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[14]  R Sevilla-Escoboza,et al.  Explosive first-order transition to synchrony in networked chaotic oscillators. , 2012, Physical review letters.

[15]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[16]  Sergio Gómez,et al.  Explosive synchronization transitions in scale-free networks. , 2011, Physical review letters.

[17]  F. Radicchi,et al.  Explosive percolation in scale-free networks. , 2009, Physical review letters.

[18]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[19]  B. Kendall,et al.  Spatial structure, environmental heterogeneity, and population dynamics: analysis of the coupled logistic map. , 1998, Theoretical population biology.

[20]  Yamir Moreno,et al.  Synchronization of Kuramoto oscillators in scale-free networks , 2004 .

[21]  J. Groff.  Exploring dynamical systems and chaos using the logistic map model of population change , 2013 .

[22]  Diego Pazó,et al.  Thermodynamic limit of the first-order phase transition in the Kuramoto model. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Martin Suter,et al.  Small World , 2002 .

[24]  S. Ellner,et al.  Chaos in Ecology: Is Mother Nature a Strange Attractor?* , 1993 .

[25]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[26]  Deok-Sun Lee.  Synchronization transition in scale-free networks: clusters of synchrony. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.