The nature of Hopf bifurcation for the Gompertz model with delays
From MaRDI portal
Publication:409877
DOI10.1016/j.mcm.2011.05.027zbMath1235.34191OpenAlexW2018290803MaRDI QIDQ409877
Monika Joanna Piotrowska, Urszula Fory's
Publication date: 15 April 2012
Published in: Mathematical and Computer Modelling (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.mcm.2011.05.027
Dynamical systems in biology (37N25) Population dynamics (general) (92D25) Cell biology (92C37) Bifurcation theory of functional-differential equations (34K18)
Related Items
Analysis of non-autonomous stochastic Gompertz model with delay, Stability of delay induced oscillations in gene expression of Hes1 protein model, Analysis of the Hopf bifurcation for the family of angiogenesis models. II: The case of two nonzero unequal delays, An immune system-tumour interactions model with discrete time delay: model analysis and validation, A streamlined numerical method to treat fractional nonlinear terminal value problems with multiple delays appearing in biomathematics, Delay Differential Equations in Bio-Populations, Tractable Model of Malignant Gliomas Immunotherapy with Discrete Time Delays, Scenarios of Critical Outbreak of Invasive Species in New Modification of Gompertz Equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A generalization of Gompertz law compatible with the Gyllenberg-Webb theory for tumour growth
- Individually-based Markov processes modeling nonlinear systems in mathematical biology
- Analysis of the Hopf bifurcation for the family of angiogenesis models
- Analysis of biochemical reactions models with delays
- Delay differential equations: with applications in population dynamics
- Critical-point analysis for three-variable cancer angiogenesis models
- Activator-inhibitor system with delay and pattern formation
- Solid tumour growth analysis of necrotic core formation
- A remark on the ODE with two discrete delays
- A time delay model about AIDS-related cancer: equilibria, cycles and chaotic behavior
- Hopf bifurcation in a solid avascular tumour growth model with two discrete delays
- Delay-induced oscillatory dynamics of tumour-immune system interaction
- Stability and bifurcations for the chronic state in Marchuk's model of an immune system
- On optimal delivery of combination therapy for tumors
- Minimizing therapeutically induced anemia
- Modeling immunotherapy of the tumor -- immune interaction
- Stability and bifurcation in delay-differential equations with two delays
- Introduction to functional differential equations
- The effect of time delays on the dynamics of avascular tumor growth
- Global analysis of Marchuk's model in a case of weak immune system
- Hopf point analysis for angiogenesis models
- Time delays in proliferation process for solid avascular tumour
- Time delays in regulatory apoptosis for solid avascular tumour
- Mathematical biology. Vol. 1: An introduction.
- Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis
- Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999)
- Delay equations. Functional-, complex-, and nonlinear analysis
- On the interaction between the immune system and an exponentially replicating pathogen
- A delay-differential equation model of HIV related cancer-immune system dynamics
- A model of immune system with time-dependent immune reactivity
- A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences
- GLOBAL ANALYSIS OF MARCZUK'S MODEL IN CASE OF STRONG IMMUNE SYSTEM
- Model of AIDS-related tumour with time delay
- ON TIME LAGS IN EQUATIONS OF GROWTH
- ANGIOGENESIS MODEL WITH CARRYING CAPACITY DEPENDING ON VESSEL DENSITY
- AntiAngiogenic Therapy in Cancer Treatment as an Optimal Control Problem
- Global stability and the Hopf bifurcation for some class of delay differential equation
- ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
- GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING
- MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS
- A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy
- Applied Delay Differential Equations
- ANTI-TUMOR IMMUNITY AND TUMOR ANTI-IMMUNITY IN A MATHEMATICAL MODEL OF TUMOR IMMUNOTHERAPY
- TUMOR-IMMUNE SYSTEM INTERACTION: MODELING THE TUMOR-STIMULATED PROLIFERATION OF EFFECTORS AND IMMUNOTHERAPY
- MATHEMATICS AND COMPLEXITY IN LIFE AND HUMAN SCIENCES
