45 citations · 85 across the 17 of their papers we have counts for
17 papers
Stability and robustness of a generalized pump-leak model for epithelial cell and lumen volume regulation
Kerry Tarrant, Alan R. Kay, Zahra Aminzare
Epithelial cells regulate ion concentrations and volume through coordinated membrane pumps, ion channels, and paracellular pathways which can be modeled by classical single-compart…
Rhythm Generation, Robustness, and Control in Stick Insect Locomotion: Modeling and Analysis
Zahra Aminzare, Jonathan E. Rubin
Stick insect stepping patterns have been studied for insights about locomotor rhythm generation and control, because the underlying neural system is relatively accessible experimen…
Spike-Adding Mechanisms in a Three-Timescale System: Insights from the FitzHugh-Nagumo Model with Periodic Forcing
Pake Melland, Rodica Curtu, Zahra Aminzare
In this work, we investigate the spike-adding mechanism in a class of three-dimensional fast-slow systems with three distinct timescales, inspired by the FitzHugh-Nagumo (FHN) mode…
Bridging the Gap between Reactivity, Contraction, and Finite-Time Lyapunov Exponents
Amirhossein Nazerian, Francesco Sorrentino, Zahra Aminzare
Reactivity, contractivity, and Lyapunov exponents are powerful tools for studying the stability properties of dynamical systems and have been extensively investigated in the litera…
Global synchronization analysis of non-diffusively coupled networks through Contraction Theory
Fatou K. Ndow, Zahra Aminzare
Synchronization of coupled dynamical systems is a widespread phenomenon in both biological and engineered networks, and understanding this behavior is crucial for controlling such…
Stochastic Logarithmic Lipschitz Constants: A Tool to Analyze Contractivity of Stochastic Differential Equations
Zahra Aminzare
We introduce the notion of stochastic logarithmic Lipschitz constants and use these constants to characterize stochastic contractivity of Itô stochastic differential equations (SDE…
Phase Reduction and Synchronization of Coupled Noisy Oscillators
Zahra Aminzare, Vaibhav Srivastava
We study the synchronization behavior of a noisy network in which each system is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all sy…
A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli
Jeungeun Park, Zahra Aminzare
Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bac…
Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons
Elizabeth N. Davison, Zahra Aminzare, Biswadip Dey +1
We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurc…
Heterogeneous inputs to central pattern generators can shape insect gaits
Zahra Aminzare, Philip Holmes
In our previous work, we studied an interconnected bursting neuron model for insect locomotion, and its corresponding phase oscillator model, which at high speed can generate stabl…
Cluster synchronization of diffusively-coupled nonlinear systems: A contraction based approach
Zahra Aminzare, Biswadip Dey, Elizabeth N. Davison +1
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the con…
Gait transitions in a phase oscillator model of an insect central pattern generator
Zahra Aminzare, Vaibhav Srivastava, Philip Holmes
Legged locomotion involves various gaits. It has been observed that fast running insects (cockroaches) employ a tripod gait with three legs lifted off the ground simultaneously in…
Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model
Jana L. Gevertz, Zahra Aminzare, Kerri-Ann Norton +3
Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy.…
Some remarks on spatial uniformity of solutions of reaction-diffusion PDE's and a related synchronization problem for ODE's
Zahra Aminzare, Eduardo D. Sontag
In this note, we present a condition which guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction-diffusion PDE with Neumann boundary conditions i…
Remarks on a population-level model of chemotaxis: advection-diffusion approximation and simulations
Zahra Aminzare, Eduardo D. Sontag
This note works out an advection-diffusion approximation to the density of a population of E. coli bacteria undergoing chemotaxis in a one-dimensional space. Simulations show the h…
Logarithmic Lipschitz norms and diffusion-induced instability
Zahra Aminzare, Eduardo D. Sontag
This paper proves that contractive ordinary differential equation systems remain contractive when diffusion is added. Thus, diffusive instabilities, in the sense of the Turing phen…
Remarks on contractions of reaction-diffusion PDE's on weighted L^2 norms
Zahra Aminzare
In [1], we showed contractivity of reaction-diffusion PDE: \frac{\partial u}{\partial t}(ω,t) = F(u(ω,t)) + DΔu(ω,t) with Neumann boundary condition, provided μ_{p,Q}(J_F (u)) < 0…