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The circle maps curve the phase response and the Arnold tongues of Consider some physical quantity ξ, which reflects the internal state of the biological oscillator. Let the eigenfrequency of the oscillator be equal T0. Let’s call a marker any event that can be clearly seen in the experiment, which is reached by the value ξ only once per period. Such a marker may be, for example, the beginning of the action potential in the cardiac preparation. Let’s define the oscillator phase as follows. The phase of an arbitrarily selected marking event (for example, the maximum value of ξ) is assumed to be zero. At any next time t, 0 < t < T0, the phase is defined as φ = t ∕ T0 (mod1). Since the rhythm is restored after the perturbation of the system, the introduced phase completely determines the state of the system.

Analysis of Dynamics of Infected Active and Uninfected Active Populations Leading to Pandemics using a Discrete Model of Two Interacting Pacemakers Taking into Account the Time of Refractoriness