Table 3 Analytic form of the core of the Triple Helix innovation systems of selected countries

Country

USA

UK

Germany

France

Core

\( \left\{\begin{array}{c}65.55\le {x}_u\le 86.06\\ {}2.80\le {x}_i\le 7.81\\ {}10.38\le {x}_g\le 28.56\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)

\( \left\{\begin{array}{c}57.48\le {x}_u\le 80.15\\ {}1.71\le {x}_i\le 5.80\\ {}17.57\le {x}_g\le 38.30\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)

\( \left\{\begin{array}{c}58.32\le {x}_u\le 84.05\\ {}1.15\le {x}_i\le 4.59\\ {}14.14\le {x}_g\le 38.84\\ {}{x}_u+{x}_{\mathrm{i}}+{x}_g=100\end{array}\right. \)

\( \left\{\begin{array}{c}33.01\le {x}_u\le 63.57\\ {}1.23\le {x}_i\le 4.69\\ {}34.10\le {x}_g\le 64.69\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)

Country

Russia

India

Brazil

China

Core

\( \left\{\begin{array}{c}21.86\le {x}_u\le 50.54\\ {}0.45\le {x}_i\le 2.10\\ {}48.30\le {x}_g\le 77.35\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)

\( \left\{\begin{array}{c}37.87\le {x}_u\le 55.87\\ {}1.78\le {x}_i\le 3.73\\ {}41.80\le {x}_g\le 59.47\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)

\( \left\{\begin{array}{c}66.36\le {x}_u\le 87.37\\ {}0.50\le {x}_i\le 2.93\\ {}11.78\le {x}_g\le 31.63\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)

\( \left\{\begin{array}{c}59.84\le {x}_u\le 82.28\\ {}0.28\le {x}_i\le 2.17\\ {}17.14\le {x}_g\le 38.81\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)