Yusuke Tone, Hiroyuki Asahara, Daisuke Ito, Tetsushi Ueta, Kazuyuki Aihara, Takuji Kousaka, Calculation Method of Local Bifurcation Point in Piecewise Nonlinear Discrete-Time Dynamical Systems, Wiley Periodicals, Inc., Electronics and Communications in Japan, Vol.99, No.3, 22-30, Feb. 2016.
Abstract: This paper proposes a method for calculation of localbifurcation points in discrete-time dynamical systems withpiecewise nonlinear characteristics (PNDDS). First, ann-dimensional PNDDS, which has two piecewise nonlinearmaps, is shown and its variational equation is derived. Next,a calculation method for the local bifurcation points thatutilizes the conditional equation for the periodic solutionand the characteristic equation is proposed. It is essential tocalculate the derivatives of the map with an initial value andwith a bifurcation parameter to obtain the bifurcation pointscontinuously in the parameter space. The above calculationprocess is a key component of the proposed method, and isexplained in detail. Finally, we apply the proposed methodto a two-dimensional PNDDS and calculate the local bifurcationpoints in order to confirm the validity of the proposedmethod.