1. Group Profile

The team currently has one Tianjin Municipal Outstanding Postgraduate Advisor, who has supervised one Tianjin Municipal Excellent Master's Thesis. The team has achieved a number of research outcomes in the theory and applications of delayed neural networks, neurodynamics, fully nonlinear partial differential equations, distributed optimization of multi-agent systems, and stochastic differential equations and dynamical systems. In the past five years, we have published numerous papers in internationally renowned academic journals, including IEEE Trans. Neural Netw. Learn. Syst., IEEE Trans. Syst. Man Cybern.: Syst., IEEE Trans. Autom. Sci. Eng., IEEE Trans. Netw. Sci. Eng., IEEE Internet Things J., Neural Netw., Inf. Sci., J. Differ. Equations, Nonlinear Dyn., and J. Math. Anal. Appl. Over the same period, we have led or participated in several research projects, including 7 projects funded by the National Natural Science Foundation of China (NSFC) and 3 projects funded by the Tianjin Natural Science Foundation. Our research encompasses the dynamics of neural networks and their applications in image encryption and reachable set estimation, as well as the other areas mentioned above, thus forming a distinctive strength that integrates multi-disciplinary basic theoretical research with practical applications.

2. Research Group Members

Professor Liqun Zhou
Academic Title：PhD Supervisor、Master Supervisor
Research Interests: Neural Network Theory and Applications
Major Achievements: Prof. Zhou has published over 100 academic papers in domestic and international journals, including IEEE Trans. Neural Netw. Learn. Syst., IEEE Trans. Syst. Man Cybern.: Syst., IEEE Trans. Autom. Sci. Eng., IEEE Trans. Netw. Sci. Eng., IEEE Internet Things J., Neural Netw., Inf. Sci., and others. In recent years, he has successfully completed one project each from the Tianjin Natural Science Foundation (General Program), the Tianjin Municipal Education Commission, and the Tianjin Teaching Reform Project. She is currently leading a General Program of the Tianjin Natural Science Foundation. She is also a Tianjin Outstanding Postgraduate Advisor and has supervised one Tianjin Municipal Excellent Postgraduate Thesis.

Associate Professor Lijie Hao
Research Interests: Neurodynamics
Major Achievements: She has published more than 10 papers in journals such as Nonlinear Dyn., Phys. Biol., Math. Biosci., etc. She has presided over and completed one Young Scientists Fund project of the National Natural Science Foundation of China (NSFC). She is currently the principal investigator of a General Program of the NSFC.

Lecturer Long Li
Research Interests: Hamiltonian Systems
 Major Achievements: He has published several academic papers in journals such as Ergod. Theor. Dyn. Syst. and Lett. Math. Phys. He has presided over and completed one Young Scientists Fund project of the National Natural Science Foundation of China (NSFC).

Associate Professor Yongkang Zhang
Research Interests: Qualitative Theory of Differential Equations, Stability of Neural Networks and Its Applications.
ajor Achievements: He has published several academic papers in journals such as Inf. Sci., Neurocomputing, Neural Comput. Appl., etc. He has also served as the principal investigator for one General Program of the National Natural Science Foundation of China (NSFC) and one General Program of the Tianjin Natural Science Foundation.

Lecturer Rong Huang
Research Interests: Approximation Theory and Stability of Neural Networks.
Major Achievements: She visited the University of Alberta, Canada, for one year during 2018–2019, and has published several academic papers in journals such as Rocky Mt. J. Math., etc.

Lecturer Fan Cui
Research Interests: Fully Nonlinear Partial Differential Equations
Major Achievements: She has published several academic papers in journals such as J. Math. Anal. Appl., Comm. Pure Appl. Anal., J. Evol. Equations, etc., and is currently the principal investigator of one National Natural Science Foundation of China (NSFC) Tianyuan Fund project and one NSFC Young Scientists Fund project.

Lecturer Na Liu
Research Interests: Multi-Agent Distributed Optimization and Neurodynamic Algorithms.
Major Achievements: She has published more than 10 papers in high-level journals such as IEEE Trans. Cybern., IEEE Trans. Autom. Control, Neural Netw., etc. She completed one sub-project of the National Key Research and Development Program as the principal investigator, and is currently leading one NSFC Young Scientists Fund project, one industry-university cooperation project, and one Tianjin Natural Science Foundation Joint Youth Fund project.

Lecturer Dandan Yang
Research Interests: Stochastic Differential Equations and Dynamical Systems, etc.
Main Achievements: Published multiple research papers in journals such as J. Differ. Equations, Stud. Appl. Math., and Appl. Math. Optim. Currently serves as Principal Investigator of one Youth Fund project funded by the Tianjin Natural Science Foundation and one Youth Program project funded by the National Natural Science Foundation of China (NSFC).

3. Representative Achievements of the Team

1. Novel Halanay inequality-based reachable set estimation for complex-valued memristive fuzzy neural networks with proportional delays
Authors: Liqun Zhou，et al.
Journal：IEEE Transactions on Neural Networks and Learning Systems, DOI: 10.1109/TNNLS.2026.3727635.

2. Distributed nonsmooth nonconvex optimization: A multiagent approach with finite-time consensus
Authors: Na Liu，et al.
Journal：IEEE Transactions on Systems, man and Cybernetics: Systmes, DOI: 10.1109/TSMC.2026.3703546.

3. Global polynomial synchronization of uncertain complex-valued reaction-diffusion T-S fuzzy memristive neural networks with proportional delays under adaptive event-triggered control
Authors: Liqun Zhou，et al.
Journal：IEEE Transactions on Neural Networks and Learning Systems, 2026，37(9): 4369-4380.

4. Asymptotic behavior of periodic measures for time-inhomogeneous fractional stochastic delay equations under domain perturbation
Authors: Dandan Yang，et al.
Journal：Journal of Differential Equations, 2026, 478: 114629.

5. Further on novel multi-state coupling and proportional distributed delays in synchronization of uncertain complex-valued state-dependent neural networks for secure communication
Authors: Liqun Zhou，et al.
Journal：IEEE Transactions on Automation Science and Engineering, 2026, 23: 9319-9332.

6. Synchronization of uncertain complex-valued antagonistic inertial state-dependent neural networks with piecewise proportional delays by event-triggered control for image encryption
Authors: Liqun Zhou，et al.
Journal：IEEE Internet of Things Journal, 2026, 13(8): 17451-17464.

7. Prescribed-time optimal resource allocation for disturbed multi-agent systems subject to limited interaction ranges
Authors: Na Liu，et al.
Journal：Communications in Nonlinear Science and Numerical Simulation，2026，161(2): 110154.

8. Global polynomial synchronization of proportional delay memristive competitive neural networks with uncertain parameters for image encryption
Authors: Liqun Zhou，et al.
Journal：IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2025, 55(10): 5424-5434.

9. A smooth gradient approximation neural network for general constrained nonsmooth nonconvex optimization problems
Authors: Na Liu，et al.
Journal：Neural Networks, 2025, 184: 107-121.

10. Adaptive pinning controller for global polynomial synchronization of inertial memristive neural networks with proportional delays and parameter perturbations for image encryption
Authors: Liqun Zhou，Na Liu，et al.
Journal：Neural Networks, 2025, 192: 107889.

11. Large deviation principles of fractional stochastic nonclassical diffusion equations on unbounded domains
Authors: Dandan Yang，et al.
Journal：Studies in Applied Mathematics, 2025, 154: e70042.

12. Dynamics and multi-scale modeling with time delays for three stages of synaptic facilitation
Authors: Lijie Hao，et al.
Journal：Nonlinear Dynamics, 2024, 112: 9531-9546.

13. Finite time blowup of solutions of the hydrostatic Euler equations
Authors: Fan Cui，et al.
Journal：Journal of Evolution Equations, 2024, 24: 81-93

14. Doubly weighted sharp Wirtinger inequalities on R+
Authors: Rong Huang，et al.
Journal：Rocky Mountain Journal of Mathematics, 2024, 54(2): 541-555.

15. Global polynomial stabilization of impulsive neural networks with bidirectional proportional delays
Authors: Liqun Zhou，et al.
Journal：IEEE Transactions on Network Science and Engineering, 2024, 1(1): 471-484.

16. Invariant measures and stochastic Liouville type theorem for non-autonomous stochastic reaction-diffusion equations
Authors: Dandan Yang，et al.
Journal：Journal of Differential Equations, 2023, 353: 225-267.

4. Introduction to the Team's Representative Research

4.1 Research Feature 1: Dynamics and Applications of Proportional Delay Neural Networks

Neural networks are an emerging interdisciplinary field, with broad applications in mathematics, computer science, artificial intelligence, information science, and other areas. Since time delays are unavoidable during network operation and due to the practical needs in the above fields, the dynamics of delayed neural networks has long been a hot research topic worldwide. Proportional delay is a type of unbounded delay. In 2011, Zhou Liqun introduced proportional delays into neural networks and established the proportional delay neural network model. Over the past decade, Zhou Liqun and his research team have devoted themselves to the in-depth study of the dynamics of proportional delay neural networks, laying a solid theoretical foundation for this area. They have systematically investigated various dynamical properties, including asymptotic stability, exponential stability, polynomial stability, periodicity, passivity, dissipativity, stabilization, and synchronization control, and have also explored their applications in image encryption and quadratic programming problems. Their research results have been published in prestigious journals in the fields of dynamics and control science, such as IEEE Trans. Neural Netw. Learn. Syst., IEEE Trans. Syst. Man Cybern.: Syst., IEEE Trans. Autom. Sci. Eng., IEEE Trans. Netw. Sci. Eng., IEEE Internet Things J., Neural Netw., Inf. Sci., among others.

4.2 Research Feature 2: Modeling and Dynamics of Memory Regulatory Mechanisms

The formation of memory has long attracted widespread attention. Synaptic plasticity is the foundation of memory formation, involving complex signaling pathways and biochemical reactions in neurons, which necessitates in-depth investigation of the underlying molecular mechanisms. In recent years, we have focused on the mathematical modeling of synaptic plasticity associated with memory formation and the analysis of its dynamical mechanisms. Specifically, we have constructed multiscale mathematical models bridging molecular and cellular levels to elucidate the dynamical principles underlying experimental observations. Furthermore, we have established a transcriptional and post-transcriptional dual regulatory network model mediated by non-coding RNAs during synaptic facilitation. Based on deterministic bifurcation theory and energy landscape theory for stochastic systems, we have revealed the global stability mechanisms behind stochastic dynamical behaviors. Related papers have been published in important journals in the field of dynamics, such as Nonlinear Dyn., Phys. Biol., among others.

4.3 Research Feature 3: Properties of Solutions to Nonlinear Partial Differential Equations, Including Monge–Ampère Type Equations

The Monge–Ampère equation is a class of fully nonlinear partial differential equations originating from affine geometry and differential geometry. It has found wide applications in geometry, physics, economics, image processing, fluid mechanics, artificial intelligence, and many other fields. In recent years, we have devoted ourselves to the study of the properties of solutions to Monge–Ampère type equations and some other nonlinear equations, including the existence of solutions, boundary regularity, finite-time blow-up, and related issues. Relevant papers have been published in journals such as J. Math. Anal. Appl., Comm. Pure Appl. Anal., and J. Evol. Equations.

4.4 Research Feature 4: Distributed Neural Dynamics Optimization for Multi-agent Systems

Distributed neural dynamics optimization for multi-agent systems integrates distributed computing, neural dynamics, and multi-agent coordination mechanisms, forming an efficient and flexible optimization framework. In this framework, each agent relies only on local information exchange without the need for global communication, which not only reduces computational burden but also enhances system robustness and scalability, making it suitable for dynamic environments such as UAV formation and smart grids. Moreover, the introduction of neural dynamics endows the framework with brain-inspired computing capabilities. By employing differential equations to simulate dynamic evolution processes, it can effectively handle nonconvex optimization problems and ensure convergence through stability theory. This approach also offers advantages in privacy preservation and parallel computing efficiency. In recent years, our team has focused on research in distributed optimization and games for multi-agent systems, and has proposed a variety of neural-dynamic methods with fast convergence. Related papers have been published in journals such as IEEE Trans. Cybern., IEEE Trans. Autom. Control, and Neural Netw.

4.5 Research Feature 5: Asymptotic Dynamics of Infinite-Dimensional Stochastic Differential Systems

Differential equations with stochastic perturbations and delay effects have wide applications in fields such as control, economics, and biology. The asymptotic dynamical behavior of their solutions is a frontier topic in the study of stochastic differential equations and infinite-dimensional dynamical systems. We have investigated the stochastic dynamical behavior of such systems through attractors, invariant measures, stability, large deviations, and related topics. Relevant papers have been published in journals such as J. Differ. Equations, Stud. Appl. Math., and Appl. Math. Optim.