## Chaotic thermal convection of couple-stress fluid layer.(English)Zbl 1390.37141

Summary: In this work we study the pattern of bifurcations and intermittent-chaos of non-Newtonian couple-stress shallow fluid layer subject to heating from below. The couple-stress parameter delays onset of convection, synchronizes chaotic behavior, and decreases the heat transfer . Some global aspects of the dynamics such as homoclinic bifurcations and transition to chaos are explored. The effects of particle size on the intermittent-chaos regime at particular normalized Rayleigh number, say $$r=166.1$$, are investigated. With the increase in couple-stress parameter, the present Lorenz-like system synchronizes to a steady state via a series of periodic solutions interspersed with intervals of chaotic behaviors.

### MSC:

 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology 37G05 Normal forms for dynamical systems 37G10 Bifurcations of singular points in dynamical systems 34D06 Synchronization of solutions to ordinary differential equations 37C29 Homoclinic and heteroclinic orbits for dynamical systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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