Magnetic fields do not induce electric fields and neither do electric fields induce magnetic fields. They are simultaneously induced by time varying currents and by time varying charges that are the sources and causes of the fields. This has been well-known since 1908 [1].
It has been since erroneously renamed as "Jefimenko's equations", see.
https://en.wikipedia.org/wiki/Jefimenko%27s_equations.
These equations have been well-known to engineers since the 1930's when Stratton and Chu published them in "Diffraction Theory of Electromagnetic Waves" Phys. Rev. July 1, 1939 vol. 56.
Professor McDonald wrote a fascinating note [2] on the subject and it should be compulsory reading to all EE/Phys majors while replacing hundreds of textbooks used in EM teaching.
Here they are reproduced in the form McDonald wrote them:
$$ \textbf{E} = \int \frac{[\rho]\hat{\textbf{n}}}{R^2}d\textbf{x}'
+\frac{1}{c}\int \frac{([\textbf {J}]\cdot \hat{\textbf{n}})\hat{\textbf{n}}+([\textbf {J}] \times \hat{\textbf{n}}) \times \hat{\textbf{n}}}{R^2}d\textbf{x}'
+ \frac{1}{c^2}\int \frac{([\dot {\textbf {J}}] \times \hat{\textbf{n}}) \times \hat{\textbf{n}}}{R}d\textbf{x}'$$
$$\textbf{B} = \frac{1}{c}\int \frac{[\textbf {J}]\times \hat{\textbf{n}}}{R^2}d\textbf{x}'
+ \frac{1}{c^2}\int \frac{[\dot {\textbf {J}}] \times \hat{\textbf{n}}}{R}d\textbf{x}'$$
In these equations the square brackets mean taking the retarded time $[f]=f(t-R/c)$.
Notice that both the electric and magnetic fields are explicitly expressed as the retarded functions of the charge density $\rho$ and current density $\textbf{J}$. In this interpretation the two "$\textrm{curl}$" Maxwell equations are restrictions as the two fields my develop but one does not induce the other, only sources create fields.
The beauty of Ignatowsky's equations is that they explicitly and separately show the reactive fields and the propagating fields. The reactive or static fields are the ones that have $1/R^2$ dependence and they are induced by charges and currents while the propagating fields have $1/R$ in the respective integrands and they induced by the time rate variation of the current density. Furthermore it is also manifestly displayed that the propagating fields are perpendicular to each other and also to the direction of propagation, i.e., the propagating field is a transverse wave and they are induced by the time rate variation of the current density.
Since a current is a moving charge, $\textbf{J}=\rho \textbf{v}$, the time rate of the current is accelerating charge, hence the propagating terms are induced by accelerating charges.
[1]: Ignatowsky: Ann. d. Physik 23, 875 (1907); 25, 99 (1908).
[2]: Kirk T. McDonald, The relation between expressions for time-dependent electromagnetic fields given by Jefimenko and by Panofsky and Phillips, American Journal of Physics 65 (11) (1997), 1074-1076