5 problems
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The multiregion singular-perturbation conjecture for intracellular calcium oscillations
The model of intracellular calcium dynamics has distinct time-scale structures in different regions of phase space: in one region the system has two fast variables and one slow var…
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The Class I model conjecture on broad-spike oscillations
The Class I model treats the concentration of IP in the cytoplasm as a parameter rather than a dynamical variable, while the original hybrid model includes interactions between…
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Persistence of aligned or connected singular-cycle families
Let and be positive perturbation parameters, and suppose that the assumptions concerning the parameters and reduced flow hold. Assume that the singularities of…
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Persistence of remote-fold singular cycles in three-timescale systems
Let the assumptions concerning the parameters, reduced flow, and slow drift hold, and suppose that the singularities of the system are remote. Let denote the system parame…
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The viscous hyperstabilization conjecture for detonation waves
For detonation waves with diffusive effects, increasing activation energy can cause unstable eigenvalues to return to the stable complex half plane. Viscous hyperstabilization conj…