Research

My research has the following directions: 

• Re-construct the reaction network structure in the setting of dynamical equivalence to find the good properties hidden in the given dynamical systems.

• Use the entropy or elliptic estimate to show the stability or the instability of equilibrium in reaction-diffusion systems.

• The asymptotic behavior of solutions for both the collisional models and the collisionless models in kinetic theory.

• Analyze the network structure in an input-output network to characterize homeostasis points in the input-output function.

Publications and Preprints

• Reaction Systems

1. 1. Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin. On the dimension of the R-Disguised toric locus of a Reaction Network. (preprint).

   2. Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea. The toric locus of a reaction network is a smooth manifold. Submitted.

   3. Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea. The structure of the moduli spaces of toric dynamical systems. Submitted.

   4. Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin. Weakly reversible deficiency one realizations of polynomial dynamical systems: an algorithmic perspective. In revision.

   5. Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin. Weakly reversible single linkage class realizations of polynomial dynamical systems: an algorithmic perspective. In revision.

   6. Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin. A Lower Bound on the Dimension of the Disguised Toric Locus. In revision.

   7. Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin. On the connectivity of the Disguised Toric Locus. In revision.

   8. Gheorghe Craciun, Jiaxin Jin, Polly Yu. An algorithm for finding weakly reversible deficiency zero realizations of polynomial dynamical systems. SIAM Journal on Applied Mathematics, 83(4), pp. 1717-1737, 2023.

   9. Gheorghe Craciun, Jiaxin Jin, Polly Yu. Single-Target Networks. Discrete & Continuous Dynamical Systems - B,  27(2), pp. 799-819, 2022.

   10. Gheorghe Craciun, Jiaxin Jin, Polly Yu. Uniqueness for the weakly reversible and deficiency zero realization. Mathematical Biosciences, 342, 108720, 2021.

   11. Gheorghe Craciun, Jiaxin Jin, Polly Yu. An efficient characterization of complex-balanced, detailed-balanced and weakly reversible system. SIAM Journal on Applied Mathematics, 80(1), pp. 183-205, 2020.

• Kinetic theory

1. 12. Jiaxin Jin, Chanwoo Kim. Stability of 3D Collisionless plasma states in constant magnetic fields with a boundary. Submitted.

   13. Jiaxin Jin, Chanwoo Kim. Boundary effect under 2D Newtonian gravity potential in the phase space. In revision.

   14. Jiaxin Jin, Chanwoo Kim. Exponential Mixing of Vlasov equations under the effect of Gravity and Boundary. Journal of Differential Equations, 366(5), pp. 645-742, 2023.

   15. Jiaxin Jin, Chanwoo Kim. Damping of kinetic transport equation with diffuse boundary condition. SIAM Journal on Mathematical Analysis, 54(5), pp. 5524-5550, 2022.

• Homeostasis in input-output networks

1. 16. Fernando Antoneli, Martin Golubitsky, Jiaxin Jin, Ian Stewart. Homeostasis in Gene Regulatory Networks. Submitted.

   17. William Duncan, Fernando Antoneli, Janet Best, Martin Golubitsky, Jiaxin Jin, Fred Nijhout, Mike Reed, Ian Stewart. Homeostasis Patterns. Submitted.

• Reaction-diffusion Systems

1. 18. Jiaxin Jin. Instability of boundary equilibrium for Reaction-Diffusion system of a complex-balanced reaction network. In revision.

   19. Gheorghe Craciun, Jiaxin Jin, Casian Pantea, Adrian Tudorascu. Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. Discrete & Continuous Dynamical Systems - B, 26(3), pp. 1305-1335, 2021.

Paper in preparation

1. 20. Fernando Antoneli, Janet Best, Martin Golubitsky, Jiaxin Jin, Homeostasis in Networks with Same Input and Output Nodes and Metal Ion Regulation. (In preparation).

   21. Gheorghe Craciun, Jiaxin Jin, Polly Yu. Dynamical equivalence to complex balancing as an open condition in parameter space. (In preparation).

   22. Jiaxin Jin, Chaojie Yuan. Positive recurrence of a stochastic model on single target networks. (In preparation).