Abstract
The article investigates a mathematical model of the Duffing oscillator with a fractional variable-order difference operator of the Caputo and convolution type. The use of new dynamic in oscillator type systems provide a new aspects and parameters in a system. The chaotic behaviour in a fractional variable order modified discrete-time Duffing system are studied numerically by phase portraits. The relationship between the order of the fractional derivative and the quality factor of the oscillatory system is established.
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