C560XL pilot reported autopilot captured a false glideslope resulting in descent below glidepath and Low Altitude Alert from ATC.

Narrative

While being vectored to the ILS XXL at ZZZ we were assigned 3;000 feet until established and were cleared for the approach. After the autopilot captured the localizer we were slightly above the glideslope and were descending slightly steeper than normal to catch the glideslope; then the glideslope rapidly centered and the autopilot captured the glideslope and began to follow it. At this time the glideslope rapidly began to deflect downward and the autopilot began a steep descent at roughly 3;000 FPM to recapture the glideslope causing the aircraft to descend below the minimum altitude published on the chart at which point the PIC and pilot flying disconnected the autopilot. At this point ATC advised us of a Low Altitude Alert and we acknowledged that we were correcting. As it was a VFR day we continued to landing with no further issues. We believe the reason for the altitude deviation was caused by a false glideslope erroneously deflecting downward which caused the autopilot to pitch down to stay on what it believed to the correct glide path.