What is the nature of power centered in men like Cardinal and Ferdinand?
The nature of power in men like Cardinal and Ferdinand is physical, coercive, and assertive with all the manifest derivatives of control, manipulation, pressure, and authority.
In The Duchess of Malfi, the Duchess is a widow whose two brothers, Ferdinand and Cardinal, feel it is their duty to order her life as they see fit. As mentioned, the nature of their power over the Duchess is:
Towards the end of Act III, Bosola, acting on Ferdinand's orders, takes the Duchess captive and forcibly brings her back to her palace. There, she is imprisoned against her will. Although Bosola assures the Duchess that her brothers mean her 'safety and pity,' their conduct suggests otherwise.
Ferdinand even prefers to see his sister in the dark. He torments her with a dead man's hand (supposedly her husband's), presents her with artificial wax figures purportedly representing Antonio and their three children, and hires madmen to afflict her with their macabre singing and dancing. In the end, the Duchess is strangled to death by executioners in Ferdinand's pay for the crime of disobeying her brothers. Her two younger children are also strangled to death. The duchess' oldest child has fled to Milan with his father, Antonio.
Over the course of the play, the duchess is coerced to bend herself to her brothers' edicts through threats to her physical safety. An example of coercion is found in Act 1 where Ferdinand threatens the Duchess with their father's dagger.
You are my sister;/ This was my father's poniard, do you see?/ I 'd be loth to see 't look rusty, 'cause 'twas his.
The dagger is a symbol of the power the brothers hold over the Duchess. They do not want her to marry because they want to inherit her estate and wealth. Both go so far as to install a spy, Bosola, in her household so that they can keep an eye on her whereabouts and actions from afar.
The brothers intend to push back, to assert if you will, their power over anything and anyone in their way. Their chief nemesis in this regard is Antonio, the man their sister has loved and married in secret. At the end of Act III, Ferdinand sends a letter to his sister demanding Antonio's head for supposedly failing to make good on some debts in Naples. The Duchess, fearing for her husband's life, advises him to flee with their oldest son to Milan.
In Act V, Antonio hopes to reconcile with his brothers-in-law, but Delio tells him that 'though they have sent their letters of safe-conduct/ For your repair to Milan, they appear/ But nets to entrap you.' In fact, the Cardinal has given the Marquis of Pescara the right to confiscate Antonio's lands and to distribute them to his own relatives or to whomever he pleases. These actions testify to the brothers' desires to completely eradicate any opposition or impediment to their plans.