. 2021 Dec 12;231(5):905–919. doi: 10.1140/epjs/s11734-021-00335-2

Table 3.

Proposed TSFLCs to stabilise chaos in FOPMs in antecedent $x_{1}$

$P_{k}$	$R_{i}$	Consequent	$P_{k}$	$R_{i}$	Consequent
$P_{0}$	$R_{1}$	$U_{1} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1123 x_{3}^{2} - 0.0491 x_{2} x_{3} + 5.912 x_{3} - \frac{x_{3}^{2}}{x_{1}} \\ - 0.0107 x_{2}^{2} + 0.0237 x_{1} x_{2} - x_{2} - \frac{0.0108 x_{3}^{3}}{x_{2}} - 1.4512 x_{3} \\ 0 \end{matrix}]$	$P_{2}$	$R_{1}$	$U_{1} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}]$ $= [\begin{matrix} 0.1581 x_{3}^{2} - 0.0688 x_{2} x_{3} + 5.912 x_{3} \\ - 0.0107 x_{2}^{2} + 0.0262 x_{1} x_{2} - x_{2} - 1.4512 x_{3} - \frac{0.0108 x_{3}^{3}}{x_{2}} \\ - 0.0108 x_{3}^{2} - x_{3} \end{matrix}]$
	$R_{2}$	$U_{2} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1123 x_{3}^{2} - 0.0491 x_{2} x_{3} + 5.912 x_{3} - 3.76 \frac{x_{3}^{2}}{x_{1}} \\ - 0.0107 x_{2}^{2} + 0.0237 x_{1} x_{2} - 2.93 x_{2} - \frac{0.0108 x_{3}^{3}}{x_{2}} - 1.4512 x_{3} \\ 0 \end{matrix}]$		$R_{2}$	$U_{2} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1581 x_{3}^{2} - 0.0688 x_{2} x_{3} + 5.912 x_{3} \\ - 0.0107 x_{2}^{2} + 0.0262 x_{1} x_{2} - 3.92 x_{2} - 1.4512 x_{3} - \frac{0.0108 x_{3}^{3}}{x_{2}} \\ - 0.0108 x_{3}^{2} - 1.4271 x_{3} \end{matrix}]$
	$R_{3}$	$U_{3} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1123 x_{3}^{2} - 0.0491 x_{2} x_{3} + 5.912 x_{3} - \frac{x_{3}^{2}}{x_{1}} \\ - 0.0107 x_{2}^{2} + 0.0237 x_{1} x_{2} - 2.93 x_{2} - \frac{0.0108 x_{3}^{3}}{x_{2}} - 1.4512 x_{3} \\ - x_{3} \end{matrix}]$		$R_{3}$	$U_{3} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1581 x_{3}^{2} - 0.0688 x_{2} x_{3} + 5.912 x_{3} \\ - 0.0107 x_{2}^{2} + 0.0262 x_{1} x_{2} - {5.98 x}_{2} - 1.4512 x_{3} - \frac{0.0108 x_{3}^{3}}{x_{2}} \\ - 0.0108 x_{3}^{2} - 1.09374 x_{3} \end{matrix}]$
$P_{1}$	$R_{1}$	$U_{1} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1231 x_{3}^{2} - 0.0528 x_{2} x_{3} + 6.9174 x_{3} \\ - 0.0107 x_{2}^{2} + 0.0237 x_{1} x_{2} - x_{2} - \frac{0.0213 x_{3}^{3}}{x_{2}} - 2.0814 x_{3} \\ 0.0013 x_{2}^{2} - x_{3} \end{matrix}]$	$P_{3}$	$R_{1}$	$U_{1} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1291 x_{3}^{2} - 0.04906 x_{2} x_{3} + 0.004 x_{1} x_{3} + 6.007 x_{3} \\ - 0.0103 x_{2}^{2} - 1.7263 x_{3} + 0.0227 x_{1} x_{2} + (0.00007) x_{2} x_{3} - x_{2} \\ - 0.0318 x_{3}^{2} - x_{3} \end{matrix}]$
	$R_{2}$	$U_{2} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] =$ $[\begin{matrix} 0.1231 x_{3}^{2} - 0.0528 x_{2} x_{3} + 6.9174 x_{3} \\ - 0.0107 x_{2}^{2} + 0.0237 x_{1} x_{2} - {4.77 x}_{2} - \frac{0.0213 x_{3}^{3}}{x_{2}} - 2.0814 x_{3} \\ 0.0013 x_{2}^{2} - {2.12 x}_{3} \end{matrix}]$		$R_{2}$	$U_{2} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1291 x_{3}^{2} - 0.04906 x_{2} x_{3} + 0.004 x_{1} x_{3} + 6.007 x_{3} \\ - 0.0103 x_{2}^{2} - 1.7263 x_{3} + 0.0227 x_{1} x_{2} + (0.00007) x_{2} x_{3} - 4.57 x_{2} \\ - 0.0318 x_{3}^{2} - 1.75 x_{3} \end{matrix}]$
	$R_{3}$	$U_{3} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] =$ $[\begin{matrix} 0.1231 x_{3}^{2} - 0.0528 x_{2} x_{3} + 6.9174 x_{3} \\ - 0.0107 x_{2}^{2} + 0.0237 x_{1} x_{2} - 1.3164 x_{2} - \frac{0.0213 x_{3}^{3}}{x_{2}} - 2.0814 x_{3} \\ 0.0013 x_{2}^{2} - 6.247 x_{3} \end{matrix}]$		$R_{3}$	$U_{3} = [\begin{matrix} u_{1} \\ u_{2} \\ u_{3} \end{matrix}] = [\begin{matrix} 0.1291 x_{3}^{2} - 0.04906 x_{2} x_{3} + 0.004 x_{1} x_{3} + 6.007 x_{3} \\ - 0.0103 x_{2}^{2} - 1.7263 x_{3} + 0.0227 x_{1} x_{2} + (0.00007) x_{2} x_{3} - 6.335 x_{2} \\ - 0.0318 x_{3}^{2} - 9.59 x_{3} \end{matrix}]$