This paper explores the phenomenon of chimera states in arrays of coupled oscillators, where the system splits into two distinct domains: one coherent and phase-locked, and the other incoherent and desynchronized. This behavior, which has never been observed in identical oscillators, cannot be attributed to spatial uniformity or non-identical oscillator frequencies. The authors focus on a ring of phase oscillators governed by a nonlocal coupling kernel, specifically a cosine kernel, to study the simplest system that supports a chimera state. They derive a self-consistency equation and solve it analytically for this system, revealing the conditions under which chimera states can exist. The analysis shows that the chimera state arises through a series of bifurcations, with the fraction of drifting oscillators decreasing as the control parameter increases. The paper also discusses the implications of this phenomenon in various spatially extended systems, including the complex Ginzburg-Landau equation and two-dimensional systems, suggesting potential applications in pattern formation.This paper explores the phenomenon of chimera states in arrays of coupled oscillators, where the system splits into two distinct domains: one coherent and phase-locked, and the other incoherent and desynchronized. This behavior, which has never been observed in identical oscillators, cannot be attributed to spatial uniformity or non-identical oscillator frequencies. The authors focus on a ring of phase oscillators governed by a nonlocal coupling kernel, specifically a cosine kernel, to study the simplest system that supports a chimera state. They derive a self-consistency equation and solve it analytically for this system, revealing the conditions under which chimera states can exist. The analysis shows that the chimera state arises through a series of bifurcations, with the fraction of drifting oscillators decreasing as the control parameter increases. The paper also discusses the implications of this phenomenon in various spatially extended systems, including the complex Ginzburg-Landau equation and two-dimensional systems, suggesting potential applications in pattern formation.