Question: In which century did the philosophy of Apollophanes of Antioch cease to flourish?

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War of the Antiochene Succession: The War of the Antiochene Succession, also known as the Antiochene War of Succession, comprised a series of armed conflicts in northern Syria between 1201 and 1219, connected to the disputed succession of Bohemond III of Antioch.  The Principality of Antioch was the leading Christian power in the region during the last decades of the 12th century, but Armenian Cilicia challenged its supremacy.  The capture of an important fortress, Bagras, in Syria by Leo II of Cilicia gave rise to a prolonged conflict already in the early 1190s.  Leo tried to capture Antioch, but the Greek and Latin burghers formed a commune and prevented the Armenian soldiers from occupying the town.  Bohemond III's eldest son, Raymond, died in 1197, leaving an infant son, Raymond-Roupen.  The boy's mother, Alice of Armenia, was LeoI's niece and heir presumptive.  BohemondIII and the Antiochene noblemen confirmed Raymond-Roupen's right to succeed his grandfather in Antioch, but the commune preferred BohemondIII's younger son (Raymond-Roupen's uncle), Bohemond, Count of Tripoli.

David Livingstone Smith: David Livingstone Smith (born 26th September 1953) is professor of philosophy at the University of New England, where he teaches philosophy of psychology, philosophy of mind, metaphysics, free will and determinism, philosophy of human nature, philosophy of race, and other topics.  He gained his MA at Antioch university and a Ph.D. in philosophy at the University of London (Kings College) where he worked on the philosophy of psychology.

Early Islamic philosophy: Early Islamic philosophy or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar (early 9th century CE) and lasting until the 6th century AH (late 12th century CE).  The period is known as the Islamic Golden Age, and the achievements of this period had a crucial influence in the development of modern philosophy and science; for Renaissance Europe, the influence represented “one of the largest technology transfers in world history.” .  This period starts with al-Kindi in the 9th century and ends with Averroes (Ibn Rushd) at the end of 12th century.  The death of Averroes effectively marks the end of a particular discipline of Islamic philosophy usually called the "Peripatetic Arabic School", and philosophical activity declined significantly in Western Islamic countries, namely in Islamic Spain and North Africa, though it persisted for much longer in the Eastern countries, in particular Persia and India where several schools of philosophy continued to flourish: Avicennism, Illuminationist philosophy, Mystical philosophy, and Transcendent theosophy.

St Symeon: St Symeon (modern name Samandağ or Suadiye) was the medieval port of Antioch, located on the mouth of the Orontes River.  It may be named after Saint Simeon Stylites the Younger, who dwelt on a mountain only six miles from St Symeon, or the original Saint Simeon Stylites, who was buried in Antioch.  Seleucia Pieria had been the Roman port of Antioch, but silting and an earthquake had rendered it unusable.  Control of St Symeon was important to the capture of Antioch by the Crusaders at the end of the eleventh century.

Stoicism: Stoicism is a school of Hellenistic philosophy that flourished throughout the Roman and Greek world until the 3rd century AD.  Stoicism is predominantly a philosophy of personal ethics which is informed by its system of logic and its views on the natural world.  According to its teachings, as social beings, the path to happiness for humans is found in accepting this moment as it presents itself, by not allowing ourselves to be controlled by our desire for pleasure or our fear of pain, by using our minds to understand the world around us and to do our part in nature's plan, and by working together and treating others in a fair and just manner.

Old River (California): The Old River is a tidal distributary of the San Joaquin River that flows for about 40 mi through the Sacramento–San Joaquin River Delta in Northern California.  The Old River was once the main channel of the San Joaquin until navigation and flood control projects in the late 19th and 20th century fixed the San Joaquin to its present course past Stockton.  It diverges from the San Joaquin near Tracy, about 38 mi upstream from Antioch, and first runs west towards Mountain House, then north to rejoin the San Joaquin 13 mi above Antioch.  The river is lined with levees that prevent flooding of the adjacent Delta islands, many of which lie below sea level.  The Middle River runs east of and roughly parallel to Old River.  False River diverges from Old River about a mile (1.6 km) above the Old River's mouth and runs westward to join the San Joaquin at a point closer to Antioch.  Part of the Old River forms the boundary between San Joaquin County on the east and Contra Costa County to the west.

John the Oxite: John VII the Oxite was the Eastern Orthodox Patriarch of Antioch at the time of the Siege of Antioch in 1097 in front of the besieging army of the First Crusade.  He was imprisoned by the Turkish governor, Yaghi-Siyan, who suspected his loyalty.  On occasion he was hung from the walls and his feet were hit by iron rods.  According to the "Historia belli sacri" (c. 1131), after the siege the Christian women of the city went to release the imprisoned patriarch, only to find that he could not stand, his legs having been weakened by so long a confinement .  He was released and re-established as Patriarch when the crusaders captured the city in 1098.  The crusaders soon established a Latin bishop in Albara (where there was no Greek bishop established) Peter of Narbonne.  Peter was consecrated by John.  The Patriarch John coexisted with Peter until John became politically inconvenient for the first Prince of Antioch, Bohemund I.  Bohemund accused him of conspiring with the Byzantine Empire, an old enemy of Bohemund and his Norman family, and John was exiled to Constantinople in 1100.  The Eastern Orthodox Church was repressed in favour of the Latin Church.  under Bernard of Valence, who succeeded Peter of Narbonne and took the position of Patriarch, establishing the line of Latin Patriarchs of Antioch.  In Constantinople, John resigned and entered a monastery in Oxia, where he wrote anti-Latin treatises.  A new Greek Patriarch was appointed in Constantinople until it was possible to restore them in Antioch later in the 12th century.

Protestantism in Cuba: While Protestants arrived in the island of Cuba early in its colonial days, most of their churches did not flourish until the 20th century with the assistance of American missionaries.  In the early 20th century, Cuban Protestant churches were greatly aided by various American missionaries who assisted in the work in the churches and also provided support from their home churches.  When Fidel Castro’s regime overtook the country in 1959, Protestant churches were legally allowed to continue.  Nevertheless, certain incidents as detailed below, and religious persecution kept them from prospering.  During the Special Period that began in 1991, Protestant churches began to flourish once again and today have become a primary religious group of Cuba.  The Protestant population of Cuba is estimated at 11%.

George II of Antioch: George II of Antioch was Eastern Orthodox Patriarch of Antioch in the 7th century.  Little is known about him except that he attended the Quinisext Council in 691–692.  It is speculated that he died of heat exhaustion caused by a long period of being outdoors.  After his death the period of Arab tolerance that had allowed the continued existence of Christianity in regions under their domination ended.  George II of Antioch's reign was one well known for peace, due to his love of many religions.  The Byzantine Empire, it is thought, worked alongside him to be able to better the Empire altogether.

Apollophanes of Antioch: Apollophanes of Antioch (Greek: Ἀπολλοφάνης ; fl.  250 BC) was a Stoic philosopher.  During his life, he left Seleucia to migrate west to Athens.  There he became a pupil and friend of Aristo of Chios.  As a student of Aristo, he may have call himself an Aristonian.  There is some assertion that he is the same as Apollophanes the physician who lived at the court of Antiochus.

Supporting paragraphs: Apollophanes of Antioch Stoicism
Answer: the 3rd century AD