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Discontinuity Induced Mixed-Mode Oscillations in a Memristive Murali-Lakshmanan-Chua Circuit
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Abstract
Mixed Mode Oscillations (MMOs) correspond to a kind of dynamic behaviour wherein the system alternates between large amplitude oscillations (LAOs) with short time scales and small amplitude oscillations (SAOs) with longer time scales as time progresses. In the present work, MMOs have been reported to occur in the memristive Murali-Lakshmanan-Chua (MMLC) circuit. The MMLC was first designed by the authors in the year 2013. It is a classical Murali-Lakshmanan-Chua circuit, wherein the Chua diode is replaced by a memristor with piece-wise linear (PWL) characteristic as its non-linearity. This memristor has two discontinuity surfaces causing the phase space of the MMLC circuit to split into three sub-regions. This also converts the MMLC circuit into a non-smooth Filippov system exhibiting Discontinuity Induced Bifurcations (DIBs) at the two switching boundaries. These DIBs lead to Mixed-Mode Oscillations (MMOs) in the circuit.
Title: Discontinuity Induced Mixed-Mode Oscillations in a Memristive Murali-Lakshmanan-Chua Circuit
Description:
Abstract
Mixed Mode Oscillations (MMOs) correspond to a kind of dynamic behaviour wherein the system alternates between large amplitude oscillations (LAOs) with short time scales and small amplitude oscillations (SAOs) with longer time scales as time progresses.
In the present work, MMOs have been reported to occur in the memristive Murali-Lakshmanan-Chua (MMLC) circuit.
The MMLC was first designed by the authors in the year 2013.
It is a classical Murali-Lakshmanan-Chua circuit, wherein the Chua diode is replaced by a memristor with piece-wise linear (PWL) characteristic as its non-linearity.
This memristor has two discontinuity surfaces causing the phase space of the MMLC circuit to split into three sub-regions.
This also converts the MMLC circuit into a non-smooth Filippov system exhibiting Discontinuity Induced Bifurcations (DIBs) at the two switching boundaries.
These DIBs lead to Mixed-Mode Oscillations (MMOs) in the circuit.
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