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
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
