Mathematical analysis of a modified Volterra-Leslie chemostat Model
Theory Biosci. 2024 Apr 9. doi: 10.1007/s12064-024-00415-6. Online ahead of print.ABSTRACTIn this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.PMID:38592425 | DOI:10.1007/s12064-024-00415-6 (Source: Theory in Biosciences)
Source: Theory in Biosciences - April 9, 2024 Category: Biology Authors: Mohammed Amine Hamra Source Type: research
Mathematical analysis of a modified Volterra-Leslie chemostat Model
Theory Biosci. 2024 Apr 9. doi: 10.1007/s12064-024-00415-6. Online ahead of print.ABSTRACTIn this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.PMID:38592425 | DOI:10.1007/s12064-024-00415-6 (Source: Theory in Biosciences)
Source: Theory in Biosciences - April 9, 2024 Category: Biology Authors: Mohammed Amine Hamra Source Type: research
Mathematical analysis of a modified Volterra-Leslie chemostat Model
Theory Biosci. 2024 Apr 9. doi: 10.1007/s12064-024-00415-6. Online ahead of print.ABSTRACTIn this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.PMID:38592425 | DOI:10.1007/s12064-024-00415-6 (Source: Theory in Biosciences)
Source: Theory in Biosciences - April 9, 2024 Category: Biology Authors: Mohammed Amine Hamra Source Type: research
Mathematical analysis of a modified Volterra-Leslie chemostat Model
Theory Biosci. 2024 Apr 9. doi: 10.1007/s12064-024-00415-6. Online ahead of print.ABSTRACTIn this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.PMID:38592425 | DOI:10.1007/s12064-024-00415-6 (Source: Theory in Biosciences)
Source: Theory in Biosciences - April 9, 2024 Category: Biology Authors: Mohammed Amine Hamra Source Type: research
Mathematical analysis of a modified Volterra-Leslie chemostat Model
Theory Biosci. 2024 Apr 9. doi: 10.1007/s12064-024-00415-6. Online ahead of print.ABSTRACTIn this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.PMID:38592425 | DOI:10.1007/s12064-024-00415-6 (Source: Theory in Biosciences)
Source: Theory in Biosciences - April 9, 2024 Category: Biology Authors: Mohammed Amine Hamra Source Type: research
Mathematical analysis of a modified Volterra-Leslie chemostat Model
Theory Biosci. 2024 Apr 9. doi: 10.1007/s12064-024-00415-6. Online ahead of print.ABSTRACTIn this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.PMID:38592425 | DOI:10.1007/s12064-024-00415-6 (Source: Theory in Biosciences)
Source: Theory in Biosciences - April 9, 2024 Category: Biology Authors: Mohammed Amine Hamra Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
Dynamics of neural fields with exponential temporal kernel
Theory Biosci. 2024 Mar 9. doi: 10.1007/s12064-024-00414-7. Online ahead of print.ABSTRACTWe consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of...
Source: Theory in Biosciences - March 9, 2024 Category: Biology Authors: Elham Shamsara Marius E Yamakou Fatihcan M Atay J ürgen Jost Source Type: research
