Bifurcation analyses of nonlinear dynamical systems: From theory to numerical computations

Dynamical ‎C‎ontrol of Computations Using the Family of Optimal Two-point Methods to Solve Nonlinear ‎Equations

One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...

Numerical Bifurcation Analysis of Dynamical Systems

Bifurcation of Switched Nonlinear Dynamical Systems

This paper proposes a method to trace bifurcation sets for a piecewise-defined differential equation. In this system, the trajectory is continuous, but it is not differentiable at break points of the characteristics. We define the Poincaré mapping by suitable local sections and local mappings, and thereby it is possible to calculate bifurcation parameter values. As an illustrated example, we an...

study of bifurcation and hyperbolicity in discrete dynamical systems

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...

Nonlinear Dynamical Systems and Kcc - Theory

Nonlinear dynamical systems can be uniquely investigated by a geometric theory (KCC-theory). The five KCC-invariants express intrinsic properties of the nonlinear dynamical systems. The second invariant as a curvature tensor determines the stability of the systems. The third invariant as a torsion tensor expresses the chaotic behavior. As an example, the KCC-theory is applied to a geodynamical ...