"The epithet 'Picasso sunflowers' triggers feelings of reverence and awe, underscoring the Spanish maestro's monumental imprint within the art realm. Picasso's sunflower cycle, executed during his Rose Period, stands as testament to his supple talent and potent imagination. These canvases, distinguished by their dynamic hues and striking contours, portray a narrative of innocence and simplicity. This discourse delves into four pivotal facets of Picasso's sunflowers: their historical relevance, artistic methodologies, societal sway, and replication dilemmas."

Chapter I - Historical Relevance of Picasso's Sunflowers

"The sunflower cycle, crafted between 1905 and 1906, occupies a distinct position in Picasso's oeuvre. It mirrors his transformation from the somber Blue Period to the radiant Rose Period, a phase marked by a shift in his color scheme from bleak, melancholy shades to vibrant, welcoming tints. The sunflowers signify optimism and rejuvenation, paralleling Picasso's personal evolution during that epoch. The cycle confers upon him the capability to encapsulate the quintessence of nature via his idiosyncratic style, rendering it a lasting emblem of his artistic prowess."

Chapter II - Artistic Methodologies in Picasso's Sunflowers

"These sunflowers asserts their singularity for their meticulous brushwork and vivacious hues. The artist deployed a range of tactics including impasto, whereby thick coats of paint are applied, and glazing, where thin layers of paint are superimposed to generate depth and texture. The audacious brushstrokes lend the flowers a tangible presence, whilst the contrasting colors accentuate their radiant charm. This section aims at elucidating the diverse strategies Picasso utilized to immortalize his iconic sunflower masterpieces."

Chapter III - Societal Sway of Picasso's Sunflowers

"Picasso's sunflowers have etched an indelible impression on the art and cultural landscape. The cycle has been replicated, scrutinized, and lauded globally, spurring numerous artists and aficionados. The sunflowers have metamorphosed into a symbol of creativity and progressiveness, encapsulating the ethos of Picasso's own artistic endeavours. This segment will probe into the societal impact of Picasso's sunflowers, encompassing their influence on modern art and mainstream culture."

Chapter IV - Reproduction Dilemmas in Picasso's Sunflowers

"Replicating Picasso's sunflowers poses specific challenges due to the artist's intricate methods and the sensitive condition of the works. The complex brush strokes and vibrant hues can prove elusive to replicate precisely, reinforcing the imperative for replications to preserve the original essence of Picasso's craftsmanship."

Picasso's sunflowers continue to mesmerize and inspire audiences worldwide, acting as a timeless tribute to the might of art. By discerning the historical weight, artistic techniques, cultural resonance, and reproduction complications of these emblematic paintings, we acquire an enriched comprehension of Picasso's genius and the enduring legacies of his creations.