In this paper we study periodic orbit bifurcation sequences in a system of two coupled Morse oscillators. Time-reversal symmetry is exploited to determine periodic orbits by iteration of symmetry lines. The permutational representation of Tsuchiya and Jaffe is employed to analyze periodic orbit configurations on the symmetry lines. Local pruning rules are formulated, and a global analysis of po...

The classical bifurcations that occur in the SIR system were already studied many papers. Our attention is focused on singular bifurcations, when has infinite number of periodic points at bifurcation limit. dynamics analyzed and results are interpreted from a practical point view.

1. Introduction. We say that a one-parameter family of diffeomorphisms ip^: M — • M, p G R, has a homoclinic bifurcation, or a homoclinic tangency, for p = 0 if ipo has an orbit of nontransverse intersection of a stable and an unstable manifold, both of the same hyperbolic fixed point (or periodic point), which splits, for p > 0, into two orbits of transverse intersection of these stable and un...

Recent studies show that hydrodynamic interactions qualitatively change the collision rate between droplets settling in a steady straining flow. We explain dependence of on non-dimensional speed by analyzing bifurcations underlying dynamical system.

We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron’s natural firing period and that of the oscillatory rhythm, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcation...