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Author ORCID Identifier



Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Jonathan Machta

Second Advisor

Karen Abbott

Third Advisor

Shubha Tewari

Fourth Advisor

Romain Vasseur

Subject Categories

Dynamical Systems | Population Biology | Statistical Models | Statistical, Nonlinear, and Soft Matter Physics


Many ecological systems exhibit noisy period-2 oscillations and, when they are spatially extended, they undergo phase transition from synchrony to incoherence in the Ising universality class. Period-2 cycles have two possible phases of oscillations and can be represented as two states in the bistable systems. Understanding the dynamics of ecological systems by representing their oscillations as bistable states and developing dynamical models using the tools from statistical physics to predict their future states is the focus of this thesis.

As the ecological oscillators with two-cycle behavior undergo phase transitions in the Ising universality class, many features of synchrony and equilibrium properties can be understood from the Ising model. However, the complete understanding of the system requires dynamical properties along with the equilibrium behavior. As memory is an important dynamical feature of ecological oscillators, we develop dynamical Ising models with memory (self-interaction) where each Ising spin has memory of its previous state. We obtain the equilibrium phase diagrams and critical lines numerically for both parallel and sequential updating and obtain analytic approximations to many of the results.

Ecological systems are commonly studied with the coupled lattice maps. Due to the presence of arbitrary local dynamics and the associated parameters, coupled lattice maps have limitations in modeling and predicting ecological behaviors. Here, we use the dynamical Ising model with memory to study the ecological oscillators by representing the two phases of oscillations as the two Ising spin states. This simplified Ising representation does a good job in representing the ecological oscillators and predicting their future states.

Ecological two-cycle oscillators may change their phase of oscillation due to noise and this transition usually occurs when the amplitude is very close to zero. As the Ising representation is limited to representing the phase of oscillations, an additional third state is required to capture the transition state dynamics. We study dynamics of a single two-cycle oscillator with various data representations and develop dynamical models from the well-studied bistable systems to predict the phase changes. We find that the transition state in the three-state representation improves the predictive accuracy of phase changes compared to the Ising representation.


Available for download on Friday, September 01, 2023