Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

Window of Chaotic Delayed Synchronization

We consider a general coupling of two chaotic dynamical systems and we obtain conditions that provide delayed synchronization. We consider four different couplings that satisfy those conditions. We define Window of Delayed Synchronization and we obtain it analytically. We use four different free chaotic dynamics in order to observe numerically the analytically predicted windows for the considered couplings.

Vector Fitting based Automatic Circuit Identification

This paper describes a method to automatically obtain, from a set of impedance measurements at different frequencies, an equivalent circuit composed of lumped elements based on the vector fitting algorithm. The method starts from the impedance measurement of the circuit and then, through the recursive use of vector fitting, identifies the circuit topology and the component values of lumped elements. The method can be expanded to include other components usually used in impedance spectroscopy. The method is firstly described and then two examples highlight the robustness of the method and showcase its applicability.