Zeitgeber and circadian activity rhythms of cockroaches a system of unipolar coupled oscillators

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Abstract
Three different patterns were found in the locomotor activity rhythm of the cockroach Leucophaea maderae, when exposed to cycles of 12 h red light: 12 h dark (RD) at constant temperature: en trainment, relative coordination, and free‐run. The different reactions were only weakly correlated with the energy ranges of the red light. Instead, the free‐running period and the previous state of the rhythm were most decisive. Entrainment to RD occurred when the free‐running period in constant conditions was close to 24 h (23.8±0.07h, SE), while animals showing shorter average period lengths in constant conditions (23.0±0.06 h or 23.0 h±0.11 h) exhibited in RD relative coordination or an unaffected free‐run, respectively. Following stepwise reduction of the red light energy to 0.5 μW/cm2, rhythms remained entrained in all cases as long as they had been entrained before, and the RD cycle was not phaseshifted. After a shift, however, re‐entrainment failed, even when the light energies were one log unit higher (5 μW/cm2). The results are consistent with properties of a system of unilaterally coupled non‐linear oscillators: the circadian rhythm reacts to RD like a driven self‐sustained pacemaker does, which is weakly coupled to a forcing oscillation.