How did the thirteen years of civil war that took place after Caesar's death end?

Before his death, Julius Caesar adopted his 18 year old
grandnephew, Octavian, as his son and made him his heir.  Octavian was away at Apollonia
when he heard of Caesar’s assassination in 44 B.C.  He immediately returned to Rome to
claim his inheritance and take power.  He was opposed by Marc Antony and Marcus Lepidus.
After battling both Antony and Lepidus, the three met and agreed to share power,
creating the Second Triumvirate. This Second Triumvirate was opposed by Marcus Junius
Brutus (Brutus) and Gaius Cassius Longinus (Cassius), two of the leaders of Caesar’s
assassination. Octavian and Antony defeated Brutus and Cassius at Philippi in 42 B.C. 
Upon defeating Brutus and Cassius, it was agreed that Octavian would rule the west,
Antony would rule the east, and Lepidus would rule Africa. Ultimately, the Second
Triumvirate would not last.  Octavian unilaterally dropped Lepidus from the Triumvirate.
The ambitions and jealousies of Antony and Octavian led to the instability of the Second
Triumvirate.  Antony, while living in the east, established an alliance with Cleopatra.
Though married, he openly lived with Cleopatra and had children with her. Octavian
turned public opinion against Antony when he acquired a copy of Antony’s will and made
it public.  It called for large legacies to his children by Cleopatra and for his burial
in Alexandria.  The Senate declared war.  Octavian’s armies defeated Antony’s and
Cleopatra’s forces at Actium in 31 B.C.  This ended the period of civil war that
followed Caesar’s assassination. Antony and Cleopatra both committed suicide. Octavian
took sole control of the Roman Empire and in 27 B.C. was awarded the title of
Augustus.