A chaotic Hartley oscillator with fractional-order JFET and its network behaviors

Non-integer (fractional)-order systems are more realistic than integer-order systems, which mimic the real-time dynamics of various physical and biological systems. As a result, in this paper, we investigate the dynamical behavior of the Hartley oscillator with fractional-order JFETs (HFJ). To begin understanding the dynamical behavior of the HFJ, we perform stability of the equilibrium point analysis, and bifurcation analysis by finding local maxima of the state variables, and Lyapunov exponents. We discover that as a function of fractional order and voltage, considered HFJ exhibits the transition from periodic to chaotic dynamics via the period-doubling route. The multistability characteristics are investigated further using forward and backward bifurcation continuations, and we exemplify the presence of distinct attractors. Finally, we demonstrate the network behavior of an HFJ system, specifically, the transition to a coherent state as increasing the magnitude of fractional order or coupling strength.