Abstract
The dynamical behaviour of non-critically finite odd transcendental meromorphic function psi(lambda)(z) = lambda sinh z/z(2) is described. Bifurcation in the dynamics of psi(lambda)(x) is shown to occur at lambda = lambda*(approximate to 2.69528), where lambda* = (x) over tilde (3)/sinh (x) over tilde and (x) over tilde is the unique positive real solution of the equation tanh x = x/3 The images of the Julia sets of psi(lambda)(z) are computer generated by using the characterization of its Julia set as the closure of the set of points with orbits escaping to infinity under iterations.