Chaotic synchronization : applications to living systems / Erik Mosekilde, Yuri Maistrenko, Dmitry Postnov.
Interacting chaotic oscillators are of interest in many areas of physics, biology, and engineering. In the biological sciences, for instance, one of the challenging problems is to understand how a group of cells or functional units, each displaying complicated nonlinear dynamic phenomena, can intera...
Singapore ; River Edge, NJ :
|Series:||World Scientific series on nonlinear science. Monographs and treatises ;
v. 42. |
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- 1. Coupled nonlinear oscillators. 1.1. The role of synchronization. 1.2. Synchronization measures. 1.3. Mode-locking of endogenous economic cycles
- 2. Transverse stability of coupled maps. 2.1. Riddling, bubbling, and on-off intermittency. 2.2. Weak stability of the synchronized chaotic state. 2.3. Formation of riddled basins of attraction. 2.4. Destabilization of low-periodic orbits. 2.5. Different riddling scenarios. 2.6. Intermingled basins of attraction. 2.7. Partial synchronization for three coupled maps
- 3. Unfolding the riddling bifurcation. 3.1. Locally and globally riddled basins of attraction. 3.2. Conditions for soft and hard riddling. 3.3. Example of a soft riddling bifurcation. 3.4. Example of a hard riddling bifurcation. 3.5. Destabilization scenario for a = a[symbol]. 3.6. Coupled intermittency-III maps. 3.7. The contact bifurcation. 3.8. Conclusions
- 4. Time-continuous systems. 4.1. Two coupled Rossler oscillators. 4.2. Transverse destabilization of low-periodic orbits. 4.3. Riddled basins. 4.4. Bifurcation scenarios for asynchronous cycles. 4.5. The role of a small parameter mismatch. 4.6. Influence of asymmetries in the coupled system. 4.7. Transverse stability of the equilibrium point. 4.8. Partial synchronization of coupled oscillators. 4.9. Clustering in a system of four coupled oscillators. 4.10. Arrays of coupled Rossler oscillators
- 5. Coupled pancreatic cells. 5.1. The insulin producing beta-cells. 5.2. The bursting cell model. 5.3. Bifurcation diagrams for the cell model. 5.4. Coupled chaotically spiking cells. 5.5. Locally riddled basins of attraction. 5.6. Globally riddled basins of attraction. 5.7. Effects of cell inhomogeneities
- 6. Chaotic phase synchronization. 6.1. Signatures of phase synchronization. 6.2. Bifurcational analysis. 6.3. Role of multistability. 6.4. Mapping approach to multistability. 6.5. Suppression of the natural dynamics. 6.6. Chaotic hierarchy in high dimensions. 6.7. A route to high-order chaos
- 7. Population dynamic systems. 7.1. A system of cascaded microbiological reactors. 7.2. The microbiological oscillator. 7.3. Nonautonomous single-pool system. 7.4. Cascaded two-pool system. 7.5. Homoclinic synchronization mechanism. 7.6. One-dimensional array of population pools. 7.7. Conclusions
- 8. Clustering of globally coupled maps. 8.1. Ensembles of coupled chaotic oscillators. 8.2. The transcritical riddling bifurcation. 8.3. Global dynamics after a transcritical riddling. 8.4. Riddling and blowout scenarios. 8.5. Influence of a parameter mismatch. 8.6. Stability of K-cluster states. 8.7. Desynchronization of the coherent chaotic state. 8.8. Formation of nearly symmetric clusters. 8.9. Transverse stability of chaotic clusters. 8.10. Strongly asymmetric two-cluster dynamics
- 9. Interacting nephrons. 9.1. Kidney pressure and flow regulation. 9.2. Single-nephron model. 9.3. Bifurcation structure of the single-nephron model. 9.4. Coupled nephrons. 9.5. Experimental results. 9.6. Phase multistability. 9.7. Transition to synchronous chaotic behavior
- 10. Coherence resonance oscillators. 10.1. But what about the noise? 10.2. Coherence resonance. 10.3. Mutual synchronization. 10.4. Forced synchronization. 10.5. Clustering of noise-induced oscillations.