Spontaneous mode switching in coupled oscillators competing for constant amounts of resources.

We propose a widely applicable scheme of coupling that models competitions among dynamical systems for fixed amounts of resources. Two oscillators coupled in this way synchronize in antiphase. Three oscillators coupled circularly show a number of oscillation modes such as rotation and partially in-phase synchronization. Intriguingly, simple oscillators in the model also produce complex behavior such as spontaneous switching among different modes. The dynamics reproduces well the spatiotemporal oscillatory behavior of a true slime mold Physarum, which is capable of computational optimization.

[1]  Kazuyuki Aihara,et al.  Resource-Competing Oscillator Network as a Model of Amoeba-Based Neurocomputer , 2009, UC.

[2]  K. Y. Michael Wong,et al.  Optimal resource allocation in random networks with transportation bandwidths , 2008, 0808.3364.

[3]  Kazuyuki Aihara,et al.  Amoeba-based Chaotic Neurocomputing: Combinatorial Optimization by Coupled Biological Oscillators , 2009, New Generation Computing.

[4]  Irving R Epstein,et al.  Diffusively coupled chemical oscillators in a microfluidic assembly. , 2008, Angewandte Chemie.

[5]  Ikkyu Aihara,et al.  Nonlinear dynamics and bifurcations of a coupled oscillator model for calling behavior of Japanese tree frogs (Hyla japonica). , 2008, Mathematical biosciences.

[6]  K. Binmore.  2. Game Theory , 2008 .

[7]  Toshiyuki Nakagaki,et al.  Amoebae anticipate periodic events. , 2008, Physical review letters.

[8]  Masashi Aono,et al.  Spontaneous deadlock breaking on amoeba-based neurocomputer , 2008, Biosyst..

[9]  Ken Binmore,et al.  Game theory - a very short introduction , 2007 .

[10]  Kazuyuki Aihara,et al.  Amoeba-based neurocomputing with chaotic dynamics , 2007, CACM.

[11]  A. Tero,et al.  Minimum-risk path finding by an adaptive amoebal network. , 2007, Physical review letters.

[12]  A Koseska,et al.  Inherent multistability in arrays of autoinducer coupled genetic oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Atsuko Takamatsu,et al.  Spontaneous switching among multiple spatio-temporal patterns in three-oscillator systems constructed with oscillatory cells of true slime mold , 2006 .

[14]  Toshiyuki Nakagaki,et al.  Physarum solver: A biologically inspired method of road-network navigation , 2006 .

[15]  Michael Small,et al.  Surrogate test to distinguish between chaotic and pseudoperiodic time series. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Evgeny A. Viktorov,et al.  Dynamics of multimode semiconductor lasers , 2003 .

[17]  B. Pompe,et al.  Permutation entropy: a natural complexity measure for time series. , 2002, Physical review letters.

[18]  E. Volkov,et al.  Multirhythmicity generated by slow variable diffusion in a ring of relaxation oscillators and noise-induced abnormal interspike variability. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[20]  Michael Small,et al.  Surrogate Test for Pseudoperiodic Time Series Data , 2001 .

[21]  T. Fujii,et al.  Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum plasmodial slime mold. , 2001, Physical review letters.

[22]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[23]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[24]  T. Nakagaki,et al.  Intelligence: Maze-solving by an amoeboid organism , 2000, Nature.

[25]  T Fujii,et al.  Time delay effect in a living coupled oscillator system with the plasmodium of Physarum polycephalum. , 2000, Physical review letters.

[26]  J. A. Kuznecov.  Elements of applied bifurcation theory , 1998 .

[27]  Schreiber,et al.  Improved Surrogate Data for Nonlinearity Tests. , 1996, Physical review letters.

[28]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[29]  Passamante,et al.  Recognizing determinism in a time series. , 1993, Physical review letters.

[30]  N. Oyama,et al.  Use of a saline oscillator as a simple nonlinear dynamical system: Rhythms, bifurcation, and entrainment , 1991 .

[31]  B. LeBaron,et al.  Nonlinear Dynamics and Stock Returns , 2021, Cycles and Chaos in Economic Equilibrium.

[32]  Richard C. Dorf,et al.  Introduction to Electric Circuits , 1989 .