This book develops a general methodological approach to investigate complex physical systems presented by the author in a previous book the nonlinear dynamics of coupled oscillators is investigated numerically and analytically. Bifurcation and chaos in coupled oscillators bifurcation diagrams are computed to show good agreement with theoretical analysis bifurcations and chaos control in dynamical systems . This paper gives an analysis of equilibria periodic solutions strange attractors of two bvp oscillators coupled by a resister when an oscillator is fixed its parameter values in nonoscillatory region and the others in oscillatory region create the double scroll attractor due to the coupling int j bifurcation and chaos . We investigate bifurcation and chaos observed in coupled bvp neurons with external impul sive forces although the single neuron without the ex ternal force has only one equilibrium point . For coupled oscillators we demonstrate full and partial synchronization patterns depending on the adjustment between the fast and slow time scales and reveal the embedded structure of the
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