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High-voltage direct-current (HVDC) system plays a vital role in enabling long-distance, bulk power transfers between regions. It is intrinsically a cyber-physical system, and is vulnerable to cyber intrusions, threatening both HVDC converters and their interconnected grids. To this end, attack-induced HVDC behaviors were investigated by identifying heterogeneous equilibrium points in the cyber-attack injection space of two-terminal line-commutated converter (LCC) HVDC systems. The combined effects of both intra-station switching control and inter-station current margin control were considered. Therein, this paper derived the closed-form cyber-attack capability boundaries by identifying the worst-case scenarios regarding power imbalance, over-current, and over-voltage. Closed-form bifurcation hyperplanes were then formulated to classify non-smooth or discontinuous attack-induced equilibrium points. They showcase an attack-induced butterfly effect of HVDC systems, where infinitesimally small cyber-attacks across bifurcation hyperplanes trigger a chain of control malfunctions. Such outcome leads to dramatic changes in the HVDC operation status, e.g., reversals in power and voltage across HVDC. Attack-induced HVDC behaviors, including the infinitesimal-attack-high-impact phenomenon, were validated by establishing a hardware-in-the-loop HVDC cybersecurity testbed using a STM32F429-based cyber-attack prototype and a Real Time Digital Simulator (RTDS).